A simple harmonic motion has amplitude A and time period T. Find the time required to travel directly from (a) x=0 to x=A/2; (b) x=0 to x=A/√2; (c) x=A to x=A/2; (d) x=-A/√2 to x=A/√2; (e) x=A/√2 to x=A.
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Question

A simple harmonic motion has amplitude A and time period T. Find the time required to travel directly from (a) x=0 to x=A/2; (b) x=0 to x=A/√2; (c) x=A to x=A/2; (d) x=-A/√2 to x=A/√2; (e) x=A/√2 to x=A.

Select all that apply

G1 Physics · Accepted Answer

Use x=A sinθ. From x=0 to A/2, Δθ=π/6 ⇒ T/12. From 0 to A/√2, Δθ=π/4 ⇒ T/8. From A to A/2, Δθ=π/3 ⇒ T/6. From −A/√2 to +A/√2, Δθ=π/2 ⇒ T/4, and from A/√2 to A, Δθ=π/4 ⇒ T/8. Therefore all four statements are correct.

A simple harmonic motion has amplitude A and time period T. Find the time required to travel directly from (a) x=0 to x=A/2; (b) x=0 to x=A/√2; (c) x=A to x=A/2; (d) x=−A/√2 to x=A/√2; (e) x=A/√2 to x=A.