A mass M is attached to the end of a spring of constant K and is set into motion

Question

A mass M is attached to the end of a spring of constant K and is set into motion by pulling it a distance A=.100 m horizontally and then releasing it. Let's agree to start our record of time the first time the mass M passes through the equilibrium position. Given A=0.100m, f=.250/s, and M=2.00kg 1.Time for one complete oscillation 2.Displacement of the mass M from the equiibrium position at t=0.5s 3.Speed of the mass M at t=1.5s 4.Acceleration of the mass m at t=2.5s 5.Total energy of the system (mass and spring) at any time.

Explanation / Answer

w = 2 * pi * 0.25 = 0.5 *pi T = 1 / f = 1 / 0.25 = 4 s equation of SHM : x = 0.1 * cos [0.5*pi*t] v = - 0.1 * 0.5 * pi * sin [ 0.5* pi * t] a = -1 * 0.25 * pi^2 * cos [ 0.5 * pi * t] Put values in above eqns and get : 2) x = 0.0999 m... 3) v = 0.00645 m/s 4) a = 0.246 m/s^2 5) E = 0.5 * m * w^2 * A ^2 = 0.02 J

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