Question

An air-track glider is attached to a spring. The glider is pulled to the right and released from rest at t = 0 s. It then oscillates with a period of 2.0 s and a maximum speed of 52 cm/s .

What is the amplitude of the oscillation?

What is the glider's position at t = 0.27 s ?

Answer 1

The glider is released as hest after pulling it to the right. At t=0, the position of glider is x= A Where A is the amplitude. At t=0 the glider is at rest. So U=0 These two conditions are satisfied by x= A coscut The velocity is time derivative of position Us - Aw sin wt The maximum velocity corresponds to smute-1 Umax = Aw It is period of oscillation 277 Using Using ع - 27 = 271 Using Umax = 52 cm/s, T=2.0s we get TA = 16.6 cm

x= Acoswt = (16.6 cm) cospat) At t= 0.275, using T= 2.03 we get x = 11cm] - 11 cm