A massless spring hangs from the ceiling with a small object attached to its lower end.The object is initially held at rest in a position yi such that the spring is at its rest length. The object is then released from yi and oscillates up and down, with its lowest position being 10 cm below yi. (a) What is the frequency of the oscillation? (b) What is the speed of the object when it is 8.0 cm below the initial position? (c) An object of mass 300 g is attached to the first object, after which the system oscillates with half the original frequency.What is the mass of the first object? (d) How far below yi is the new equilibrium (rest) position with both objects attached to the spring?
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 massless spring hangs from the ceiling with a small object
attached to its lower end.The object is initially held at rest in a
position yi such that the spring is at its rest length. The object is
then released from yi and oscillates up and down, with its lowest
position being 10 cm below yi. (a) What is the frequency of the oscillation?
(b) What is the speed of the object when it is 8.0 cm below
the initial position? (c) An object of mass 300 g is attached to
the first object, after which the system oscillates with half the original
frequency.What is the mass of the first object? (d) How far below
yi is the new equilibrium (rest) position with both objects attached
to the spring?
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