Question

A light spring is suspended with mass '\(m_1\)' at its lower end and its upper end is fixed to a rigid support. The mass is pulled down a short distance and then released. The period of oscillation is T second. When a mass '\(m_2\)' is added to '\(m_1\)' and the system is made to oscillate the period is found to be \(\frac{3}{2}\) T. The ratio \((\frac{m_1}{m_2})\) is

• A. \(2:3\)
• B. \(3:4\)
• C. \(4:5\)
• D. \(5:6\)

Hint:

Write each in the form A sin(wt + phi) and compare the phase angles.

Answer 1

The Correct Option is C

Step 1: Observe the ratio:
$x_2 = \sqrt2\,x_1$ for every t, because $x_2$ is just $\sqrt2$ times the expression of $x_1$.

Step 2: Meaning:
One function is a constant multiple of the other, so they reach maximum and zero together. The phase difference is zero (A).

Final Answer:
Zero. \[ \boxed{0} \]