Oscillations

JEE Main level, single correct, medium

65 of 194

Question 65 of 194

A point mass oscillates along the xx-axis according to the law x=x0cos⁡(ωt−π/4)\mathrm{x=x_0 \cos (\omega t-\pi / 4)}. If the acceleration of the particle is written as
a=Acos⁡(ωt+δ)\mathrm{a=A \cos (\omega t+\delta)}

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Answer: (D) A=x0ω2,δ=3π/4\mathrm{A=x_0 \omega^2, \delta=3 \pi / 4}

v=−x0ωsin⁡(ωt−π/4)\mathrm{v=-x_0 \omega \sin (\omega t-\pi / 4)}
a=−x0ω2cos⁡(ωt+π−π4)\mathrm{a=-x_0 \omega^2 \cos \left(\omega t+\pi-\frac{\pi}{4}\right)}
a=Acos⁡(ωt+δ)\mathrm{a=A \cos (\omega t+\delta)}
A=x0ω2;δ=3π4\mathrm{A=x_0 \omega^2 ; \quad \delta=\frac{3 \pi}{4}}

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