Question

A block oscillating on a spring has period T1 = 2.38s . Note that you do not know the value of either m or k, so do not assume any particular values for them. The required analysis involves thinking about ratios.

Part A: What is the period if the block's mass is doubled?
Part C: The value of the spring constant is quadrupled?
Part E:The oscillation amplitude is doubled while m and k are unchanged?

Answer 1

Theformula for timeperiod of oscillation is given by:

\(T=2 \pi \sqrt{\frac{m}{k}}\)

Thus, if mass is doubled,

T increases by a factor of sqrt (2)

Tnew \(=3.36 \mathrm{sec}\)

If \(\mathrm{k}\) is quadrupled, the timeperiod is reduced by a factor of \(\operatorname{sqrt}(4)=2\)

Thus, Tnew \(=2.38 / 2=1.19 \mathrm{sec}\)

Amplitude has no impact on time period.

Thus, changing amplitde does not change the time period.