A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of $$3s$$. When the mass m is increased by $$1$$ kg, the time period of oscillations becomes $$5$$ s. The value of m in kg is

Question

A body of mass  m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass  m is slightly pulled down and released, it oscillates with a time period of $$3s$$. When the mass  m is increased by $$1$$ kg, the time period of oscillations becomes $$5$$ s. The value of  m in kg is

Infinity Learn · Accepted Answer

Time period of spring $$-$$ block system, $$T=2$$$$π$$mk For given spring, T∝$$mT1T2=m1m2$$ Here, $$T1=3$$ s,$$m1=m$$,$$T2=5$$ s,$$m2=m+1$$,$$m=$$?$$35=mm+1$$ or, $$925=mm+125$$ $$m=9$$ $$m+9$$⇒$$16$$ $$m=9$$⇒$$m=916$$ kg

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