Question

5. A mass-spring system oscillates with an amplitude of 3.5 cm. If the spring constant is 250 N/m and the mass is 0.50 kg, a) Write an equation for the position, velocity, and acceleration for the mass as a function of time b) find the maximum speed of the mass, and the maximum acceleration of the mass. c) Sketch a plot of the position of the mass vs time by labelling the values for amplitude and period.

Answer 1

(a)k = 250 N/M m = .50 kg A = 3.5 cm F = -kx m = d^2/dt^2 = -kx d^x/dt^2 + k/m x = 0 w = squareroot k/m w = squareroot 250/5 = 22.36 rad /s x(t) = A sin wt velocity v(t) = d x(t)/dt v(t) = dx (t)/dt v(t) = Aw co swt a(t) = d^2 x(t)/dt^2 a(t) = -Aw^2 sin wt (b) max speed v_0 = Aw = .035 times 22.36 = .7826 m/s = 78.26 cm/s a_0 = Aw^2 = .035 times 22.36 times 22.36 = 17.5 m/s^2 (c)