A point mass oscillates along the x-axis according to the law x=x0cos ωt-π4. If the acceleration of the particle is written as a=A cos ωt+δ,then :

A point mass oscillates along the x-axis according to the law $x = x_{0} \cos (ωt - \frac{π}{4})$ . If the acceleration of the particle is written as $a = A \cos (ωt + δ),$ then :

A
$A = x_{o} ω^{2}, δ = \frac{3 π}{4}$
B
$A = x_{o}, δ = - \frac{π}{4}$
C
$A = x_{o} ω^{2}, δ = \frac{π}{4}$
D
$A = x_{o} ω^{2}, δ = - \frac{π}{4}$

Solution:

Acceleration,
$a = \frac{d^{2} x}{{dt}^{2}} = - x_{0} ω^{2} \cos (ωt - \frac{π}{4}) = x_{0} ω^{2} \cos (ωt - \frac{π}{4} + π) = x_{0} ω^{2} \cos (ωt + \frac{3 π}{4}) \Rightarrow A = x_{0} ω^{2} and δ = \frac{3 π}{4}$

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