A ball of radius R=25cm and mass M=0.43kg is compressed against a spring of spring constant k=316N/m by an amount x=49.7cm measured from the equilibrium of the spring as shown in the figure below. The system is released from rest and when the spring reaches its equilibrium position the ball loses contact with the spring. Assume the ball rolls without slipping along the 0=29° incline after it is released. Find the translational speed of the ball after it travels d= 70.4cm from the point of losing contact with the spring. Isphere =2/5 MR2. Take g=9.8 m/s2 and express your answer using two decimal places.
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.
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