A spring with a constant k=42.3 N/m has a 2.10 kg mass attached to it. The mass

Question

A spring with a constant k=42.3 N/m has a 2.10 kg mass attached to it. The mass is free to slide on a frictionless track parallel to the spring. The mass is displaced from its equilibrium position back 0.726 m (so x(0)= -0.726 m) and released at t= 0.00 s.

1. Write down an expression for the position of the mass as a function of time. Make sure that your expression has x(0)= -0.726 m, to agree with the initial condition.

2. What is the velocity of the mass at a time t= 3.70 s? Hint: make sure your calculator is in radian mode when calculating the trig function.

3. What is the maximum acceleration experienced by the mass?

4. What is the total energy in the system?

Explanation / Answer

1) x(t) = -0.726*cos(wt )

w = sqrt(k/m) = sqrt(42.3/2.1)=4.49

x(t) = -0.726*cos(4.49*t)

2) v = dx/dt = 0.726*4.49*sin(4.49*3.7)=-2.56 m/s

3) max a = w^2 A = 4.49^2*0.726= 14.64

4) max E = 1/2 k A^2 = 0.5*42.3*0.726^2=11.15 J

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