A block of mass m is attached to the end of an ideal spring. Due to the weight o

Question

A block of mass m 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 from its equilibrium length. (Figure 1) The spring has an unknown spring constant k.

Part A

What is the spring constant k?

Express the spring constant in terms of given quantities and g, the magnitude of the acceleration due to gravity.

Part B

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

Express the frequency in terms of given quantities and g, the magnitude of the acceleration due to gravity.

Explanation / Answer

Here ,

part A) for the block to be at rest

k * x = m g

k * h = m*g

k = m*g/h

the spring constant is m*g/h

part B)

for the oscillations ,

angular frequency ,w = sqrt(k/m)

w = sqrt(m*g/(h*m))

w = sqrt(g/h)

the angular frequency of the block's motion is sqrt(g/h)

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