Restoring force for a pendulum at angle theta is given by which expression?

• A. F_restoring = m g sin(theta)
• B. F_restoring = - m g sin(theta)
• C. F_restoring = m g cos(theta)
• D. F_restoring = - m g cos(theta)

Answer: (A)

The restoring force comes from the part of gravity that acts along the swing’s path toward the lowest point. When the pendulum is displaced by an angle θ from vertical, gravity has a tangential component of magnitude m g sin θ pulling it back toward θ = 0. This is why the restoring force’s magnitude involves sin θ. The cos θ component goes radially toward the pivot and affects tension rather than pulling the pendulum back along its arc. If you track direction with a sign, the restoring force along the angular direction would be - m g sin θ, but as a magnitude the restoring force is m g sin θ.