x (cm) 2.00 1.00 0.00 -1.00 -2.00 1 2 3 4 5 (a) For this motion, find the amplitude. cm (b) For this motion, find the period. s (c) For this motion, find the angular frequency. rad/s (d) For this motion, find the maximum speed. cm/s t (s) (e) For this motion, find the maximum acceleration. cm/s²
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.
![**Simple Harmonic Motion of a Spring-Mass System**
An object attached to a spring vibrates with simple harmonic motion, as illustrated in the graph below.
**Graph Description:**
- **Axes:**
- The horizontal axis represents time \( t \) in seconds (s), ranging from 0 to 6 seconds.
- The vertical axis represents displacement \( x \) in centimeters (cm), ranging from -2.00 cm to 2.00 cm.
- **Graph Characteristics:**
- The graph shows a sinusoidal wave with peaks at \( x = 2.00 \) cm and troughs at \( x = -2.00 \) cm.
- The graph indicates complete cycles between the time intervals of 0 to 3 seconds and 3 to 6 seconds.
**Tasks:**
(a) For this motion, find the amplitude.
[Answer: ____ cm]
(b) For this motion, find the period.
[Answer: ____ s]
(c) For this motion, find the angular frequency.
[Answer: ____ rad/s]
(d) For this motion, find the maximum speed.
[Answer: ____ cm/s]
(e) For this motion, find the maximum acceleration.
[Answer: ____ cm/s\(^2\)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59577f62-52f2-4d8a-8fce-f8969dac81ff%2F94f1ae87-028e-4892-b879-3bfab7f160e9%2Fn43fnl6a_processed.png&w=3840&q=75)
According to question we need to find---
- (a) For this motion, find the amplitude.
- (b) For this motion, find the period.
- (c) For this motion, find the angular frequency.
- (d) For this motion, find the maximum speed.
- (e) For this motion, find the maximum acceleration.
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