Question

A particle moving about its equilibrium position with equation y = -ax - bt. Interpret the condition

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

A particle moving about its equilibrium position with equation y = - ax - bt. Interpret the condition

(a) It will always perform the SHM.

(b) It can never perform the SHM.

(c) It can perform SHM only when t ≥ bx/a.

(d) It can perform SHM only when t ≤ bx/a.

EVALUATION

Here it is given that the particle moving about its equilibrium position with equation y = - ax - bt

So the equation is

$\displaystyle \sf{y = - ax - bt}$

Differentiating both sides with respect to t we get

$\displaystyle \sf{ \frac{dy}{dt} = - a \frac{dx}{dt} - b}$

Again Differentiating both sides with respect to t we get

$\displaystyle \sf{ \frac{{d}^{2} y}{d {t}^{2} } = - a \frac{{d}^{2} x}{d {t}^{2} } } \: \: \: - - - - (1)$

Now the equation of a simple harmonic motion ( SHM ) is

$\displaystyle \sf{ \frac{{d}^{2} x}{d {t}^{2} } = - { \omega}^{2} x } \: \: \: - - - - (2)$

Equation 1 and Equation 2 can never be same

So the given equation can never perform the SHM.

FINAL ANSWER

Hence the correct option is

(b) It can never perform the SHM

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