A 2.6 block oscillates on a spring with spring constant 22 . At = 0 the block is

Question

A 2.6 block oscillates on a spring with spring constant 22 . At = 0 the block is 20 to the right of the equilibrium position and moving to the left at a speed of 100 . Determine the period of the oscillation. Determine the amplitude of the oscillation. Can you show work too

Explanation / Answer

x = a cos (wt) a=amplitude, w=2pi/Period =angu. speed ----------------- check equ with boundary conditions>> v = speed = dx/dt = -a w sin(wt) t=0, v = 0 >>as sin (o) =0 >released from rest >> OK ------------------------------------- max speed >> v(max) will be at mean position (x=0) >> 0 = a cos (wt) cos (wt) = so sin (wt) =1 at v(max) |v-max| = aw [remember this] 20.5 (cm/s) = a *2pi/T = a *2pi/11.9 a = 20.5*11.9/2*3.14 = 38.85 centimeter amplitude = 38.85 cm --------------------- x = a cos (wt) at given t = 0.632 s x = 38.85 cos [2pi *0.632/11.9] x = 38.85 cos [0.3335] = 38.85*0.945 x = 36.71 cm

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