A uniform square plate of edge length a is suspended from one of its corners. Calculate the time period of small oscillations for this plate.

Step-by-step solution

The time period of a physical pendulum is given by T = 2 I mgd , where I is the moment of inertia about the axis of suspension and d is the distance from the point of suspension to the center of mass. For a square plate of edge length a suspended from a corner, the distance to the center of mass is half the diagonal: d = a 2 The moment of inertia of the square plate about an axis passing through its center of mass and perpendicular to its plane is: I_ cm = m(a^2 + a^2) 12 = ma^2 6 Using the parallel axis theorem, t