Question

A block oscillating on a spring has period T = 2.2 s . Note: You do not know values for either m or k. 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 quadrupled? Express your answer with the appropriate units. T =

Part B What is the period if the value of the spring constant is tripled?

What is the period if the oscillation amplitude is quadrupled while m and k are unchanged?

Answer 1

Period of oscillation is given by :

T = 2*pi*sqrt(m/k)

where , m = mass

k = spring constant

We can clearly see that T is proportional to sqrt(m)

So, if m is quadrupled (4 times), T becomes = sqrt(4) = 2 times

So, new period , T' = 2*2.2 = 4.4 s

B)

Similarly, If spring constant is tripled, T becomes = 1/sqrt(3) times.

So, new time constant , T'' = 2.2/sqrt(3) = 1.27 s <---------- answer

C)

As period doesnt depend on amplitude of the oscillation, the period will remain same when amplitude is quadrupled.