Two light springs of force constants k 1 and k 2 and a very small block of mass m are in one line AB on smooth horizontal table such that one end of each spring is fixed on rigid supports and the

Question

Two light springs of force constants k 1 ​ and k 2 ​ and a very small block of mass m are in one line AB on 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 springs is 60 cm. If the block moves along AB with a velocity 120 cm/s in between the springs, calculate the period of oscillation (in sec) of the block.

TestHub · Accepted Answer

The block executes a half-cycle with each spring and travels freely across the 60 cm gap twice.

$T = π \frac{m}{k _{1}} + π \frac{m}{k _{2}} + \frac{2 d}{v}$

Substitution gives approximately 2.83 s.

Accepted range: 2.80 to 2.85.

Physics - SHM Question with Solution | TestHub

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