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

Explanation / Answer

You have the position as a function of time: x(t)

To find the velocity, take the derivative of the position function to get v(t) and then just plug in the desired t-values.

To find the acceleration, take the derivative again to get a(t) and then plug in the desired t-values.

So just to get you started, x(t) = A*sin(2?t/T) the derivative of this is:
v(t) = A*2?/T*cos(2?t/T)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.