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.
![1.
A small ball is attached to a wall by two identical springs as shown below.
lllll-
If the ball was released at a x = xo (small displacement from equilibrium position)
(a)
with O velocity, what is the oscillation frequency?
(b)
released at x =
With a damping force F = -bv and a driving force F = Fosin (wt), the ball was
xo with 0 velocity, what is x(t) in the steady state? (You do not need to solve
the equation from scratch. You can find the answer based on your notes.)
In (b), if the ball was released at x = -x, with 0 velocity, what is the steady state
(c)
x(t)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad652258-9903-4747-b271-a85a8265e6a7%2F99448234-5ceb-4a0d-8f13-834a6d857722%2Fckrhtju_processed.png&w=3840&q=75)
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