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.
(B) The energy is defined by E=(1/2) mv2+(1/2) kx2 where k=4(pi)2m/T2. The initial energy is E0=3.20  J. Calculate the energy at t = T/4 and T/2.

Explanation / Answer

x(t) = A sin(2(pi)t/T)

velocity = dx/dt = A x 2pi / T cos (2(pi)t/T)

put in the values of T and find answer

accelration = dv/dt = A x [2(pi)/T]^2 x - sin (2(pi)t/T)

put in the values of T and find answer

as enrgy is neither created nor destroyed the total energy will remain conserved = 3.2 J

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