Two masses, each having a value of M, are vibrating vertically on a spring with a Hooke's law constant, k. At the lowest point of the vibration, one of the masses falls off, so that now the total mass is M instead of 2M. Comparing the new vibrational motion to the original vibrational motion: 1) How is the period of vibration different, if at all? Explain you reasoning. 2) How is the maximum acceleration different, if at all? Explain your reasoning. 3) How is the maximum velocity different, if at all? Explain your reasoning. Quantitative comparisons are preferred: i.e., one-third as large or twice as fast.
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.
Two masses, each having a value of M, are vibrating vertically on a spring with a Hooke's law constant, k. At the lowest point of the vibration, one of the masses falls off, so that now the total mass is M instead of 2M.
Comparing the new vibrational motion to the original vibrational motion:
1) How is the period of vibration different, if at all? Explain you reasoning.
2) How is the maximum acceleration different, if at all? Explain your reasoning.
3) How is the maximum velocity different, if at all? Explain your reasoning.
Quantitative comparisons are preferred: i.e., one-third as large or twice as fast.
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