First slide

Simple hormonic motion

Question

A particle of mass m = 2kg executes SHM in xy plane between points A and B under the action of a force $\vec{F} = (F_{x} \hat{i} + F_{y} \hat{j}) .$ Minimum time taken by the particle to move from A to B is 1 second. At t = 0, the particle is at x = 2 and y = 2. Then $F_{x}$ as function of time t is

Moderate

A

$- 4 π^{2} \sin π t$
B

$- 4 π^{2} \cos π t$
C

$4 π^{2} \cos π t$
D

None of these

Solution

T = Time period = (1 + 1) S = 2S
$\begin{array}{l} ∴ ω = \frac{2 π}{T} = π \sec . E q u a t i o n o f S H M i s x = A \cos ω t . \\ ∴ F_{x} = - m ω^{2} x = - m ω^{2} A \cos ω t = - 2 \times π^{2} \times 2 \cos π t = - 4 π^{2} c o s π t \end{array}$

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