Name: Velocity and Acceleration in SHM
Uploaded: 2019-07-19
Duration: 5 min 47 s
Description: In this video, we will derive the equations and graphs of the velocity and acceleration of an object in SHM. Let us watch this video now.

Question

A physical pendulum consists of two meter-long sticks joined together as shown in the figure shown below. What is the pendulum's period of oscillation about a pin inserted through point $A$ at the center of the horizontal stick?

Accepted Answer

The time period of a compound pendulum is given by,
$T = 2 π \sqrt{\frac{I}{m g h}}$
where, $I$ is the moment of inertia, $m$ is the mass of the pendulum and $h$ is the distance between the pivot point and the center of mass.

Given, length of each sticks is, $L = 1 m$ . The sticks are identical and hence, have equal mass, $M$ . The center of mass of the horizontal stick is at $A$ while that of the vertical is at a distance, $L / 2$ from $A$ . Thus, the center of mass of the combined system with reference to point $A$ will be, $\frac{(0 + \frac{L}{2})}{2} = \frac{L}{4}$ .

Now, the moment of inertia of the system will be,
$I = \frac{1}{12} M L^{2} + \frac{1}{3} M L^{2} = \frac{5}{12} M L^{2}$ .

Therefore, the time period will be,
$T = 2 π \sqrt{\frac{(\frac{5}{12} M L^{2})}{(\frac{(2 M) g L}{4})}} = 2 π \sqrt{\frac{5 L}{6 g}} = 1.83 s$ .

A physical pendulum consists of two meter-long sticks joined together as shown in the figure shown below. What is the pendulum's period of oscillation about a pin inserted through point $A$ at the center of the horizontal stick?

Important Questions on Oscillations

Learn and Prepare for any exam you want !

A physical pendulum consists of two meter-long sticks joined together as shown in the figure shown below. What is the pendulum's period of oscillation about a pin inserted through point A at the center of the horizontal stick?

Important Questions on Oscillations

Learn and Prepare for any exam you want !

A physical pendulum consists of two meter-long sticks joined together as shown in the figure shown below. What is the pendulum's period of oscillation about a pin inserted through point $A$ at the center of the horizontal stick?