A block of mass m is attached to one end of a spring. The other end of the sprin

Question

A block of mass m is attached to one end of a spring. The other end of the spring is fixed. The block slides without friction along a line (the x-axis) on a horizontal surface. The equilibrium position of the block is x = 0. As a function of time, x(t) = A sin(2(pi)t/T) where T = 2.43 s and A = 0.17 m.
(A) Calculate the velocity at t = 0, T/4 and T/2.

(B) Calculate the acceleration at t = 0, T/4 and T/2.

please work out problem completely as I have been having trouble coming up with the correct answer.

Explanation / Answer

x(t) = A sin(2(pi)t/T) where T = 2.43 s and A = 0.17 m.

w=2pi/T =2.584 rad/s

a)

velocity v=dx/dt =A*2*pi/T *cos(2pi*t/T)=Aw cos(2*pi*t/T) =0.17*2.584 cos(2*pi*t/T)

at t = 0

v=0.439 m/s

at t=T/4

v = 0.17*2.584 cos(2*pi*t/T) = 0

at t= T/2

v =-0.439 m/s

b)

acceleration a =Aw^2 sin(2*pi*t/T)

at t =0

a = 0

at t =T/4

a =Aw^2 =1.135 m/s^2

at t=T/2

a =0

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