A particle executes two perpendicular SHMs given by x = 3cos5t and y = 4sin5t, where x and y are in metres and t is in seconds. If its maximum resultant speed is N m/s, find N.

Question

G1 Physics · Accepted Answer

Velocity components are vₓ = −15sin5t, vᵧ = 20cos5t. Therefore, v² = 225sin²5t+400cos²5t. The maximum value occurs when cos²5t = 1. Thus, vₘₐₓ² = 400, so vₘₐₓ = 20 m/s. Hence, N = 20.