When a 1.3kg mass was attached to a spring, the spring stretched 21cm from its equilibrium position. The mass spring system was then set into oscillatory motion by providing the mass with an initial velocity. Its oscillatory motion is then described by the following equation: Y(t) = (0.09m) sin(2π t/T + π/3).

Question

When a 1.3kg mass was attached to a spring, the spring stretched 21cm from its equilibrium position. The mass spring system was then set into oscillatory motion by providing the mass with an initial velocity. Its oscillatory motion is then described by the following equation:  Y(t)  = (0.09m) sin(2π t/T + π/3).

(a) find the maximum speed (in m/s)

(b) maximum acceleration of the mass (in m/s2),

(c) Find the position of the mass at t = 0 s in meters.

(d) Find the speed of the mass at t = 0 s in meters

(e) Find the mechanical energy of the system relative to the equilibrium position at t = 0 s.

Part e is really hard for me to find.

Damon · Answer

The mechanical energy of the system is the sum of kinetic and potential energy. In this ideal world it does not change with time. Since you found the maximum speed use (1/2) m v^2