A 1.50 kg ball is attached to a vertical spring with a spring constant of 15.00 N/m. From the spring’s unstrained length, the ball is released and it vibrates in simple harmonic motion (no air resistance). (a) How far (distance) does the ball fall just before it is brought to a momentary stop by the spring? (b) How far from the unstrained length is the equlibrium position? (c) What is the maximum speed vmax of the ball everytime it approaches the equilibrium position? (d) What is the total potential energy (gravitational and elastic) of the ball at 0.50 m above the equilibrium position?
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 1.50 kg ball is attached to a vertical spring with a spring constant of 15.00 N/m. From the spring’s unstrained length, the ball is released and it vibrates in
(a) How far (distance) does the ball fall just before it is brought to a momentary stop by the spring?
(b) How far from the unstrained length is the equlibrium position?
(c) What is the maximum speed vmax of the ball everytime it approaches the equilibrium position?
(d) What is the total potential energy (gravitational and elastic) of the ball at 0.50 m above the
equilibrium position?
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