An air-track glider is attached to a spring. The glider is pulled to the right a

Question

An air-track glider is attached to a spring. The glider is pulled to the right and released from rest at t=0 { m s}. It then oscillates with a period of 1.50s and a maximum speed of 42.0cm/s . What is the amplitude of the oscillation? What is the glider's position at t= 28.0s ?

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] 42 (cm/s) = a *2pi/T = a *2pi/1.5 a = 42*1.5/2*3.14 = 38.85 centimeter amplitude = 10.03 cm --------------------- x = a cos (wt) at given t = 28 s x = 10.03 cos [2pi *28/1.5] x = 5.53 cm

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