The maximum energy of a vibrating mass is 3.00 x 10-2 joules. The amplitude of the oscillation is 2.50 mm with a frequency of 200 Hz. What is the mass of the object? What is the maximum acceleration of the object? If the mass affects the vibration frequency (like that of a mass and spring system), what should the mass be to double the maximum energy? Assume that the oscillation amplitude is not affected.
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.
The maximum energy of a vibrating mass is 3.00 x 10-2 joules. The amplitude of the oscillation is 2.50 mm with a frequency of 200 Hz.
- What is the mass of the object?
- What is the maximum acceleration of the object?
- If the mass affects the vibration frequency (like that of a mass and spring system), what should the mass be to double the maximum energy? Assume that the oscillation amplitude is not affected.
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