Question

A block of mass 40 grams is suspended from an ideal spring and set into vertical oscillations. Find the mass to be added on the spring such that the period of oscillation increases by 25%.

Answer 1

T = `2π sqrt(m/k)  i.e., T α sqrtm`

∴ `(T_2)/T_1 = sqrt(m_2/m_1)`

∴ `(1.25T_1)/T_1 = sqrt((m_1 + x)/m_1)`

∴ `(m_1 + x)/m_1 = 1.25 xx 1.25`

∴ x = (40 × 1.25 × 1.25) − 40

= (50 × 1.25) − 40

= 62.5 − 40

= 22.5 g