Topic: Theory of Machines
A mass m is attached to two identical springs having stiffness k as shown in figure below. The natural frequency of the vibrating system is
- A. (1/2pi) * $\sqrt{k/m}$
- B. (1/2pi) * $\sqrt{2k/m}$
- C. (1/2pi) * $\sqrt{k/2m}$
- D. (1/2pi) * $\sqrt{4k/m}$
Answer: B. (1/2pi) * $\sqrt{2k/m}$
Explanation: The two springs are attached to fixed supports on either side of the mass. When the mass is displaced by x, both springs exert a restoring force of kx in the same direction. Thus, they act in parallel. Equivalent stiffness K_eq = k + k = 2k. Natural frequency = (1/2pi) * $\sqrt{2k/m}$.