A block of mass m = 4.00 kg is attached to the end of an ideal spring. Due to th

Question

A block of mass m= 4.00 kg is attached to the end of an ideal spring. Due to the weight of the block, the block remains at rest when the spring is stretched a distance h= 10.0 cm from its equilibrium length. (Figure 1) The spring has an unknown spring constant k. Take the acceleration due to gravity to be g = 9.81 m/s2 .

A)What is the spring constant k?

B)Suppose that the block gets bumped and undergoes a small vertical displacement. Find the resulting angular frequency of the block's oscillations about its equilibrium position.

Explanation / Answer

A) Apply, Hook's law

F = k*x (here x is extension of the spring)

m*g = k*x

==> k = m*g/x

= 4*9.81/0.1

= 392.4 N/m

B) angular frequency, w = sqrt(k/m) (here k is spring constant and m is mass)

w = sqrt(392.4/4)

= 9.9 rad/s

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