The two pendulums shown in (Figure 1) each consist of a uniform solid ball of mass M supported by a massless string, but the ball for pendulum A is very tiny while the ball fo pendulum B is much larger.
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.
- Find the period of pendulum A for small displacements.
- Find the period of pendulum B for small displacements.
![The image features two scenarios involving pendulums.
**Diagram A:**
- Shows a simple pendulum system.
- A small mass, labeled \( M \), is suspended from a fixed horizontal support \( A \).
- The length of the pendulum from the support to the mass is marked as \( L \).
**Diagram B:**
- Illustrates a larger spherical mass, labeled \( M \), also suspended from a fixed horizontal support \( B \).
- The distance from the support to the top of the sphere is \( L \).
- The diameter of the sphere is shown, indicating that the center of mass is located at an additional distance of \( L/2 \) from the bottom of the suspension.
These diagrams are used to compare different pendulum setups focusing on the position of the mass and its effect on the pendulum's dynamics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffca80790-8a56-4ae2-a9ca-b268cf0b0359%2Fd9d736af-1c39-4784-ae25-06f0f8eaebc9%2Fxeqg6s9_processed.png&w=3840&q=75)
![The two pendulums shown in (Figure 1) each consist of a uniform solid ball of mass \( M \) supported by a massless string, but the ball for pendulum \( A \) is very tiny while the ball for pendulum \( B \) is much larger.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffca80790-8a56-4ae2-a9ca-b268cf0b0359%2Fd9d736af-1c39-4784-ae25-06f0f8eaebc9%2Fnfnqmx_processed.png&w=3840&q=75)
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