A block of mass M oscillating with amplitude A on a frictionless horizon force constant k. The period of its oscillations is T. At the moment when the block is at position x= the right, a ball of clay of mass m dropped from above lands on the block.
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.
![3. A block of mass M oscillating with amplitude A on a frictionless horizontal table is connected to an ideal spring of
force constant k. The period of its oscillations is T. At the moment when the block is at position x=
the right, a ball of clay of mass m dropped from above lands on the block.
A and moving to
2
M
x=-A
x= 0
x= A
x=A
(а)
What is the velocity of the block just before the clay hits?
(b)
What is the velocity of the block just after the clay hits?
(c)
What is the new period of the oscillations of the block?
(d)
What is the new amplitude of the oscillations? Write your answer in terms of A, k, M, and m.
(e)
Would the answer to part (c) be different if the clay had landed on the block when it was at a different position?
Support your answer briefly.
(f)
Would the answer to part (d) be different if the clay had landed on the block when it was at a different position?
Support your answer briefly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6ea7d026-9753-49d7-bda3-2ce1625fea57%2Fedac5516-81f6-4771-a4db-05d303ca9c27%2F5zix2nj_processed.jpeg&w=3840&q=75)
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