A mass is attached to the end of a spring and set into simple harmonic motion with an amplitude A on a horizontal frictionless surface. Determine the following in terms of only the variable A. (a) Magnitude of the position (in terms of A) of the oscillating mass when its speed is 30% of its maximum value. (b) Magnitude of the position (in terms of A) of the oscillating mass when the elastic potential energy of the spring is 30% of the total energy of the oscillating system.
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.
A mass is attached to the end of a spring and set into simple harmonic motion with an amplitude A on a horizontal frictionless surface. Determine the following in terms of only the variable A.
(a) Magnitude of the position (in terms of A) of the oscillating mass when its speed is 30% of its maximum value.
(b) Magnitude of the position (in terms of A) of the oscillating mass when the elastic potential energy of the spring is 30% of the total energy of the oscillating system.
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