What will be the periodic time of the block, between the two springs?

Question

As shown in figure, two light springs having force constants k1 = 1.8Nm–1 and k2 = 3.2Nm–1 and a block having mass m = 200g are placed on a frictionless horizontal surface. One end of both springs are attached to rigid supports. The distance between the free ends of the spring is 60 cm and the block is moving in this gap with a speed v = 120 cm *–1.

What will be the periodic time of the block, between the two springs?

(A) 1 + (5π/6)*

(B) 1 + (7π/6)*

(C) 1 + (5π/12)*

(D) 1 + (7π/12)*

Answer 1

The correct option (D) 1 + (7π/12)s

Explanation:

t3 = time to travel from D to C = {(Distance Dc)/(Velocity)} = (60/120)

= (1/2) sec.

t4 = time to travel from C to D = {(Distance DC)/(Velocity)} = {60/120}

= (1/2) sec

∴ Time to complete 1 oscillation = t3 + t4 + t1 + t2

= (1/2) + (1/2) + (π/3) + (π/4)

= 1 + (7π/12) sec