A mass suspended from a vertical spring performs S.H.M. of period 0 1 second. The spring is unstretched at the highest point of suspension. Maxmimum speed of the mass is (Gravitational acceleration . g =10 ~m / s ^2 )

Step-by-step solution

The maximum speed in simple harmonic motion is given by v_ max = A , where A is the amplitude and the angular frequency. For a mass-spring system, = 2 / T . With T = 0.1 , s , it follows that = 20 , rad/s . At the equilibrium position, kx₀ = mg , so x₀ = mg/k . The spring is unstretched at the highest point, confirming that the amplitude A = x₀ = mg/k . The period also gives T = 2 m/k , so m/k = (T / (2 ))^2 = 1/(400 ^2) . Combining these, v_ max = A = (mg/k) = g (m/k) . Substituting g = 10 , m/s ^2 , m/k = 1/(400