First slide

Applications of SHM

Question

One end of a spring of force constant k is fixed to a vertical wall and the other to a block of mass m resting on a smooth horizontal surface. There is another wall at a distance x₀from the block. The spring is then compressed by 2x₀ and released. The time taken to strike the wall is

Difficult

A

$\frac{1}{6} π \sqrt{\frac{k}{m}}$
B

$\sqrt{\frac{k}{m}}$
C

$\frac{2 π}{3} \sqrt{\frac{m}{k}}$
D

$\frac{π}{4} \sqrt{\frac{k}{m}}$

Solution

The total time from A to C
$t_{A C} = t_{A B} + t = (T / 4) + t_{B C}$
where T = time period of oscillation of spring mass system
$t_{B C} can be obtained from, B C = A B \sin (2 π / T) t_{B C}$
$Putting \frac{B C}{A B} = \frac{1}{2} we obtain t_{B C} = \frac{T}{12}$
$\Rightarrow t_{A C} = \frac{T}{4} + \frac{T}{12} = \frac{2 π}{3} \sqrt{\frac{m}{k}}$ .

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