Question

A mass m is suspended from the two coupled springs connected in series. The force constant for springs are $k_1$ and $k_2$. The time period of the suspended mass will be

• A. T = 2 $\pi \sqrt{ \frac{ m}{ k_1 - k_2 }}$
• B. T = 2 $\pi \sqrt{ \frac{ m k_1 k_2}{ k_1 + k_2 }}$
• C. T = 2 $\pi \sqrt{ \frac{ m}{ k_1 + k_2 }}$
• D. T = 2 $\pi \sqrt{ \frac{ m ( k_1 + k_2)}{ k_1k_2 }}$

Answer 1

Answer: (D)

T = 2 $\pi \sqrt{ \frac{ m ( k_1 + k_2)}{ k_1k_2 }}$

Answer 2

The effective spring constant of two springs in series is k = $\frac{ k_1 k_2 }{ k_1 + k_2 }$
Time period, T = 2 $\pi \sqrt{ \frac{ m}{ k}} = 2 \pi \sqrt{ \frac{ m ( k_1 + k_2)}{ k_1 k_2}}$