Question

A block of known mass is suspended from a fixed support through a light spring. Can you find the time period of vertical oscillation only by measuring the extension of the spring when the block is in equilibrium?

Answer 1

Answer ⇒ Yes, I can find time period by knowing the extension in the spring only.  

  T = 2π√x/g, where x is the extension.

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Explanation ⇒ As we know,

Time period = 2π √m/k,

where k is the Spring Constant.

Now,

When the system is in equilibrium, then,

net force will be zero.

There are two forces, acting on the system.

1.  Force of Gravity (Vertically downwards).

2. Force of the Spring (Vertically Upwards).

∴ Net Force = mg - kx

∴ mg = kx [Since, net Force = 0]

∴ k = mg/x

where, x is the extension in the spring.

Now, substituting the value of k in Time period formula.

Time period = 2π √m/(mg/x) =  2π√x/g

∴ T = 2π√x/g

Hope it helps.