Question

Two particles performing simple harmonic motions of maximum accelerations, \(1\) m/s\({}^{2}\) and \(100\) m/s\({}^{2}\), have the same amplitudes. The ratio of their angular frequencies is

• A. \(1:100\)
• B. \(1:10\)
• C. \(1:1000\)
• D. \(1:1\)

Hint:

Maximum acceleration equals omega squared times amplitude, and the amplitudes are the same.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Maximum acceleration in SHM: \(a_{max}=\omega^2A\).

Step 2: Ratio
With equal amplitude: \(\dfrac{a_1}{a_2}=\dfrac{\omega_1^2}{\omega_2^2}=\dfrac{1}{100}\)

Step 3: Take the square root
\(\dfrac{\omega_1}{\omega_2}=\dfrac{1}{10}\)

Final Answer:
The ratio of angular frequencies is 1 to 10. \[ \boxed{\text{(B) }1:10} \]