A spring stretches 0.350 m when a 0.750 kg mass is hung from it. The spring is then stretched an additional 0.250 m from this equilibrium point and released. Determine (a) the spring constant, k, (b) the maximum velocity of the mass, (c) the maximum acceleration of the mass, (d) the total (mechanical) energy of the mass, (e) the period and frequency of the mass and spring and (e) the equation of the time dependent vertical position of the mass.
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.
Given that
The mass hung from the spring (m) = 0.750Kg
it is stretches (xo) = 0.350m
the amplitude of the system is
A = 0.250m
The spring constant is given by
Putting all the given values in the above equation , we get
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