Does air resistance increase or decrease the period of a simple pendulum?
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In my physics notes, it has been given that the damping force increases the period of oscillation. I am unable to understand this part. How is this possible? The only relation I know is that as the damping force increases the amplitude decrease. But how does this contribute to increased time period of oscillation?
59488
This is quoted from A.P.French's Vibrations &amp; Waves:  If the driving force is of low frequency  relative to the natural frequency, we would expect the particle to move essentially with the driving force. This is equivalent in saying that $m\dfrac{d^2x}{dt^2}$ in $$m\dfrac{d^2x}{dt^2} + kx = F_0\cos\omega t$$ plays small role compared to the term $kx$. The amplitude is controlled by spring constant. On the other hand, at frequencies very large compared to the natural frequency, the opposite situation holds. The $kx$ becomes small compared to $m\dfrac{d^2x}{dt^2}$. In this case, we expect a relatively smaller amplitude of oscillation than the above case.  $\bullet$ Why does $kx$ become prominent in the first case &amp; not in the second case? $\bullet$ What is the physical reason behind that the first case has greater amplitude &amp; the second one smaller?
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I've been pondering the precise mechanism of time dilation for the example of a simple pendulum in two different situations:   The observer and ground are at rest in one frame of reference;  the pendulum is moving at high speed with respect to that frame. The observer is at rest in one frame of reference; the pendulum and the ground together move at high speed with respect to that frame.   user8260 has pointed out that in situation 1, in the pendulum's frame $g$ is greater by $\gamma^2$ compared to $g$ in the observer's frame. Thus in the pendulum's frame the period is less than it is in the observer's frame by a factor of $1/\gamma$, just as one would expect from time dilation.  But what about situation 2? Here, compared to the pendulum frame, the observer sees the pendulum with the same length in a stronger gravitational field, yet observes a longer period. Does the inertial mass of the pendulum change differently than its gravitational mass? Also, does the analysis depend on whether the plane of swing is perpendicular or parallel the direction of motion?
90102
Related:   I was learning about GPS satellite orbits and came across that Low Earth Orbits () have a period of about 88 minutes at an altitude of 160 km.  When I took a mechanics course a couple of years ago, we were assigned a problem that assumed that if one could drill a hole through the middle of the Earth and then drop an object into it, what would your period of oscillation be? It just happens to be a number that I remembered and it was 84.5 minutes (see ). So if I fine-tuned the LEO orbit to a vanishing altitude, in theory, I could get its period to be 84.5 minutes as well. Of course, I am ignoring air drag.  My question is: why are these two periods (oscillating through the earth and a zero altitude LEO) the same? I am sure that there is some fundamental physical reason that I am missing here. Help.
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It has come to the point in my computing program now where I have 5 swinging pendulums that are all modified at once by slider values. These values are drawn onto the from and passed through the class pendulum. To change the values the update button is run, and their is a default option to use a setup that works. The values are also shown on screen through some simple labels. The zero button sets all values (except length) to zero.  The values for each pendulum drawn is:   String length angle Acceleration (angular) Angluar velocity Damping or friction Gravity   My calcuations for these values: (Bob = the weight at the end of the string, and there are X and Y Co-ordiantes for it.  bobX = originX + (Math.Sin(angle) * length);         bobY = originY +(Math.Cos(angle) * length);   Caclulate Acceleration:  Angular Acceleration = (-1 * gravity / length) * Math.Sin(angle);    Increment Velocity:          Angular Velocity += Angluar Acceleration;   Increment Angle          angle += AngularVelocity;   Friction action, pendulum eventually 0's          AngularVelocity*= damping;   Now my next task is to make the pendulums collide "realistically" and recreate a newtons cradle type effect. I've looked into elastic collision solutions on particle e.g. here is an excellent example:    I've also looked at the raw physics behind it  but my brain couldn't get to grips with the raw physics side of things.  So I'm wondering if anybody could help me figuring out the theory for the collisions.  My current idea is when the co-ordinates meet the velocity will simply change polarity e.g. +10 to -10 in the opposing pendulum. Am I correct here?  If you are into code I've posted the code on stack overflow
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Intro:  In completing , he presents an experiment (go to 42:44) which leaves me baffled.    Experiment:  (I recommend watching the video; see link above.)   There is a $2$ kg block with 2 identical strings attached to it: one at the top, the other at the bottom. The top string is attached to a "ceiling", and the bottom to a "floor". Professor Lewin "stretches" the system (by pulling on the bottom string) with the block not accelerating. One string snaps.     Prediction:   Initially, the top string has a tension of approximately $20$ N, to counter the force of gravity. The bottom string has no tension at all. Then, when Lewin pulls the bottom string, it gains some tension $n$ N. To counter act the force exerted by the bottom string, the top string exerts now $20 + n$ N. I assume that the string with more force will give out sooner, leading me to conclude that the top string will break.     Results:  (This was conducted by Lewin, not me; see link above.)   Trial 1: Bottom string breaks. Trial 2: Top string breaks. Trial 3: Bottom string breaks.     Additional Notes:  The results don't seem consistent. If I was right, I'd expect all 3 experiments to be right; conversely, if I was wrong, I'd expect all 3 experiments wrong, with one exception: the results are more-less random and one result isn't preferred over the other.    Question:        Why was my prediction incorrect?   Was there a flaw in my logic?   Why were the results inconsistent?
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I am given an initial x and y position and initial velocity and I was asked to graph the trajectory in 1 second intervals.  This is what I have so far:  If $x_0 = 1, v_{0x} = 70, y_0 = 0, v_{0y} = 80, a_x = 0, a_y = -9.8$, and time will be 0,1,2,3... and so on.  Using these equations on every second you can find the plot will be a bell shaped with the highest point being ~ 325 m at about 600 seconds:   $$ x = x0 + (v_{0x})t + 1/2((a_x)t^2) $$ $$ y = y0 + (v_{0y})t + 1/2((a_y)t^2) $$  Usually in physics, we are taught in perfect condition with no air resistance. But what if there was air resistance? How would it affect this problem? How can i add it to my calculations and see what the difference is?
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Do Euler-Lagrange equations hold only for inertial systems? If yes, where is the point in the variational derivation from Hamilton's principle where we made that restriction? My question arose because I was thinking how could you describe the motion of pendulum with an oscillating suspension point, something like this:  If you take your coordinate frame fixed in the suspension point, you would get the motion of a simple pendulum, which is false (because it's a non-inertial frame and you should have virtual forces). But if it were moving at constant speed, a moving coordinate frame should give the same equations of motion. So where does the restriction to non-inertial frames come from in the Lagrangian formalism? I've read that in non-inertial frames the lagrangian would be $L(q,\dot q, \ddot q, \dddot q..., t)$, but I didn't see a detailed explanation. And I'm not sure if the situation would be similar to Kepler's problem in polar coordinates.
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When two bodies, free of movement, are linked by a physical constraint (a maximum distance between them) how do their masses and velocities influence each other? Which formula with theses parameters gives the force applied by one of the two on the other?  For example : I have two box (grey and red) that are next to each other attached by a rope of maximum length L, the grey one jump following the yellow curve C and i'm trying to get the equation to find the force applied to the red box when the distance between the boxes reach L. V is the velocity when the gray box reach the red circle. It would probably split into the radial force and the tangential force depending on the angle. I guess the answer would probably work for every position on the red circle.  I tried to read about pendulum but there was only the gravity taken into consideration, and it kinda felt like the tension was vertical. There might be an answer for me in one ticket but i just couldn't find it.
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I'm looking for an intuition on the relationship between time period and amplitude (for a small pertubation) of pendulums.  Why does the period not depend on the amplitude? I know the math of the problem. I am looking for physical intuition.
59538
A ball is shot directly upward, and then it comes back to the place where it was shot. Suppose we have air resistance. Suppose $t_1$ is the time period from the moment that the ball was shot to the moment that it reached its highest altitude, and $t_2$ is the time period from the moment it reached its highest altitude to the moment it reached its original position. Is $t_1=t_2$? Why or why not?
10573
I have been looking for this for quite some time now. A simple pendulum behaves in SHM. Let's put that pendulum in an upward accelerating elevator. The component of the force that acts in SHM $(\text{mg}\sin\theta)$ still stays the same in my head.  However, websites and books tell me to use $m(g+a)\sin\theta$ where $a$ is the acceleration of the elevator.  I tried to look up Free Body Diagrams, but I can't find any for the case of accelerating frames. Can someone explicitly prove this without using the flimsy argument of "Think it's a noninertial frame with a new effective g"?
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When a rubber ball bounces, it first accelerates in the positive direction (downward) then it bounces (hits the floor) .The velocity then becomes negative as the ball declerates while travelling upward - accelerates in the negative direction. After some time, the velocity is finally cancelled out by the downward force of gravity on the ball.  At this point the same amount of force pushing the ball upward is the same pushing it downward - it is at zero velocity.  My question is, how long does this period of zero velocity (motionlessness) last.
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How do  keep going? The pendulum is what makes the clock go. However, the pendulum will slow down due to friction. What energy source keeps the pendulum from eventually stopping?
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If an object is moving at terminal velocity and then opens the parachute, the air resistance is higher than the weight so why doesnt he go upwards.
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Is there a relationship between these 2   As of now I am moving a piece blutac up and down a ruler to change my COG. I have connected the base of my ruler to a vibration generator and am measuring the highest amplitude to measure the resonance frequency.   The closer the COG is to to the base the higher my resonance frequency is.
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A  posted on Youtube.  How does this phenomenon work? I know he is using frequency to propagate water in a sine/cosine wave, but how does it exactly work this way? Why do we see it as if its paused, or in slow motion, or even in reverse?  Can someone please explain this? I am intrigued by the video and want to know it's physics.