A block with mass m =7 kg is hung from a vertical spring. When the mass hangs in

Question

A block with mass m =7 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.2 m. While at this equilibrium position, the mass is then given an initial push downward at v = 4.2 m/s. The block oscillates on the spring without friction.

1) What is the spring constant of the spring?

2) What is the oscillation frequency?

3) After t = 0.32 s what is the speed of the block?

4) What is the magnitude of the maximum acceleration of the block?

5) At t = 0.32 s what is the magnitude of the net force on the block?

A block with mass m =7 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.2 m. While at this equilibrium position, the mass is then given an initial push downward at v = 4.2 m/s. The block oscillates on the spring without friction. 1) What is the spring constant of the spring? 2) What is the oscillation frequency? 3) After t = 0.32 s what is the speed of the block? 4) What is the magnitude of the maximum acceleration of the block? 5) At t = 0.32 s what is the magnitude of the net force on the block?

Explanation / Answer

a)

in equillibrium kx = mg

k*0.2 = 7*9.81

k=343 N/m

b) 2 pi f = sqrt(k/m)

2*pi*f = sqrt(343/7)

f= 1.11 Hz

c) v = vmax cos( w t) = -4.2*cos(2*pi*1.11*0.32)= 2.58 m/s

d) max a = vmax w = 4.2*2*pi*1.11= 29.3 m/s^2

e) Fnet = k x = k v/w = 343*2.58/(2*pi*1.11)= 127 N

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