= 12.5° during its motion. How far does the pendulum bob me ball at the end of the rope) travel in one complete cycle motion if its length is r = 53.1 cm? istance: x10 TOOLS cm 0
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.
![The pendulum shown in the figure sweeps out an angle of \( \theta = 12.5^\circ \) during its motion. How far does the pendulum bob (the ball at the end of the rope) travel in one complete cycle of motion if its length is \( r = 53.1 \) cm?
**Distance:** \_\_\_\_\_ cm
**Tools:**
- Multiplication by 10 (x10)
**Diagram Explanation:**
The diagram illustrates a pendulum with a string of length \( r \). The pendulum bob is swinging, making an angle \( \theta \) of \( 12.5^\circ \) with the vertical. The path of the pendulum, indicated by the arc, is part of a circle with radius \( r \).
To solve this problem, you would calculate the arc length for one complete cycle, which is twice the arc length swept by the angle \( \theta \). Use the formula for arc length:
\[ s = 2 \times \left(\frac{\theta \times \pi}{180}\right) \times r \]
where \( \theta \) is in degrees, and \( r \) is the pendulum length.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb8635a0-8b2a-40cb-87d0-b22d177615a6%2F2a79748b-a61b-4b64-b0f1-057ff754bc94%2Fj95e08a_processed.jpeg&w=3840&q=75)
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