Question

Two springs one of force constant $100N/m$ and the other of $300N/m$ are joined vertically one above the other and hung from a support at top. A mass of $3kg$ is attached to the lower spring. The time period for simple harmonic motion of such a system is :

• A. $40\pi /100$
• B. $20\pi \sqrt{3}/200$
• C. $20\pi /\sqrt{3}$
• D. $40\pi /\sqrt{3}$

Answer 1

The correct option is A $40\pi /100$

The third period for simple harmonic motion of such a system.
$T=2\pi \sqrt{\frac{(k_1+k_2)m}{k_1{k}_2}}$
$=2\pi \sqrt{\frac{(100+300)\times 3}{100\times 300}}$
$=2\pi \sqrt{\frac{3\times 400}{100\times 300}}$
$=\frac{40\pi }{100}$.