Question

A block of mass 4kg is attached to a spring of spring constant 100 N/m. One end of spring is attached to the
roof. Initially the block is at rest. When released maximum speed attained by the block is
(a) 2
(b) 4
(C)3
(d) 2.5
​

Answer 1

answer : option (a) 2

explanation : first of all, find amplitude (maximum displacement through mean position).

at equilibrium,

weight of body = spring force

or, mg = k.A, where A is amplitude and K is spring constant.

here, m = 4kg, g = 10m/s² , k = 100N/m

so, A = mg/k = (4kg × 10m/s²)/(100N/m)

= 0.4 m

now angular momentum, $\omega$= √{k/m}

= √{100/4} = 5 rad/s

so, maximum speed attained by block, v = $\omega A$

= 5 × 0.4 = 2 m/s

hence, option (a) is correct choice.