Question

A block oscillating on a spring has period T = 2.8 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.)(a) What is the period if the block's mass is doubled?(b) What is the period if the value of the spring constant is doubled?(c) What is the period if the oscillation amplitude is halved while m and k are unchanged?

Answer 1

Answer:

Part a)

T = 3.96 s

Part b)

T = 1.98 s

Part c)

T = 2.8 s

Explanation:

As we know that time period of spring block system is given as

$T = 2\pi\sqrt{\frac{m}{k}}$

T = 2.8 s

Part a)

If the mass of the block attached is doubled

then we will have

$T' = 2\pi\sqrt{\frac{2m}{k}}$

$T' = \sqrt2 T$

$T' = 3.96 s$

Part b)

If the spring constant is doubled

then we have

$T' = 2\pi\sqrt{\frac{m}{2k}}$

$T' = \frac{T}{\sqrt2}$

$T' = 1.98 s$

Part c)

If the amplitude is halved but mass and spring constant will remain the same

so here we know that time period does not depends on Amplitude

so we will have

$T = 2\pi\sqrt{\frac{m}{k}}$

T = 2.8 s