You are swinging a sling shot, which is basically a string tied to a rock, vertically as shown. After you get it going fairly fast, you hold your hand stationary so it swings around in a perfect circle. The rock slows down as it gets higher and speeds up as it comes back down. One simple model for how this would work is that the tangential component of the rock's velocity is vt(t)=v0-(v0/4)sin((2pi/T)t) where v0 is the rock's speed at t=0s and T is the time it takes the rock to go all the way around the circle. Call L the length of the string. 1. What is the total acceleration
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
You are swinging a sling shot, which is basically a string tied to a rock, vertically as shown. After you get it going fairly fast, you hold your hand stationary so it swings around in a perfect circle.
The rock slows down as it gets higher and speeds up as it comes back down. One simple model for how this would work is that the tangential component of the rock's velocity is
vt(t)=v0-(v0/4)sin((2pi/T)t)
where v0 is the rock's speed at t=0s and T is the time it takes the rock to go all the way around the circle. Call
L the length of the string.
1. What is the total acceleration of the rock?
2. What is the
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