Topic: Theory of Machines / Vibrations
A mass m attached to a light spring oscillates with a period of 2 sec. If the mass is increased by 2 kg, the period increases by 1 sec. The value of m is-
- A. 1 kg
- B. 1.6 kg
- C. 2 kg
- D. 2.4 kg
Answer: B. 1.6 kg
Explanation: Given Mass = m, Time period $T_{1}=2$ sec. Mass is increased by 2 kg $=m+2$, Time period increases $T_{2}=2+1=3$ sec. Time period, $T_{1}=2\pi\sqrt{\frac{m}{k}}=2$ ...(i). Mass increases by 2 kg, Time period, $T_{2}=2\pi\sqrt{\frac{m+2}{k}}=3$ ...(ii). From equation (i) and (ii): $\sqrt{\frac{m}{m+2}}=\frac{2}{3} \Rightarrow \frac{m}{m+2}=\frac{4}{9} \Rightarrow 9m=4m+8 \Rightarrow 5m=8 \Rightarrow m=1.6$ kg.