Problem 4. A block of mass 2.00 kg is attached to an ideal spring placed on a ho

Question

Problem 4. A block of mass 2.00 kg is attached to an ideal spring placed on a horizontal, frictionless surface. The other end of the spring is fixed. A horizontal force of 20.0 N is required to hold the block at rest when it is pulled 0.200 m from its equilibrium position. The object is released from this position and undergoes SHM. (a) What is the spring constant of the spring? (b) What is the frequency (f) of the oscillations? (c) What is the maximum speed of the block? d) Where in the motion does the block have its maximum speed? (e) What is the maximum magnitude of the acceleration of the block? (f) Where does it occur? (g) What is the total energy of the system? (h) What is the speed and acceleration of the block when its position is equal to one third of the maximum value?

Explanation / Answer

#a)

K = F/x = 20/0.2 = 100 N/m

b)

w = sqrt(k/m) = 7.07 /s

f = w/1pi = 1.125 hz

c)Vmax = A*w = 0.2*7.07 = 1.414 m/s

d) at equilibrium position

e)a = w^2*A = 9.99698 m/s^2

f) at extreme point i.e at 0.2m

g) TE = 0.5*K*A^2 = 0.5*100*0.2*0.2 = 2J

h) TE = 0.5*m*v^2 + 0.5*K*x^2

2 = 0.5*2*v^2 + 0.5*100*(0.2/3)^2

v = 1.33 m/s

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