A mass m attached to free end of a spring executes SHM with a period of 1 s . If the mass is increased by 3 kg the period of oscillation increases by one second, the value of mass m is ________ kg .

Step-by-step solution

Time period of oscillation is given by T = 2 π m k , where k is the force constant of the spring. ∵ Spring is same, therefore, spring constant will be same. Putting the different values, In the first case T = 1 = 2 π m k In the second case T ' = 2 = 2 π m + 3 k Dividing the equations, we get T T ' = 1 2 = m m + 3 ⇒ m m + 3 = 1 4 ⇒ 4 m = m + 3 ⇒ m = 1 Thus, m = 1   kg