Simple Harmonic Motion 4 Question 16

16. Two light springs of force constants k1 and k2 and a block of mass m are in one line AB on a smooth horizontal table such that one end of each spring is fixed on rigid supports and the other end is free as shown in the figure.

The distance CD between the free ends of the spring is 60cm. If the block moves along AB with a velocity 120cm/s in between the springs, calculate the period of oscillation of the block. (Take, k1=1.8N/m,k2=3.2N/m,m=200g)(1985,6M)

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Answer:

Correct Answer: 16. 2.82s

Solution:

  1. Between C and D block will move with constant speed of 120cm/s. Therefore, period of oscillation will be (starting from C ).

T=tCD+T22+tDC+T12

Here, T1=2πmk1 and T2=2πmk2

and tCD=tDC=60120=0.5s

T=0.5+2π20.23.2+0.5+2π20.21.8

(m=200g=0.2kg)

T=2.82s



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