A particle is executing simple harmonic motion. Its amplitude is A and time period is 5 sec

Question

A particle is executing simple harmonic motion. Its amplitude is A and time period is 5 sec. The time required by it to move from $x = A$ to $x = \frac{A}{\sqrt{2}}$ is _________ sec. [2026]

Smart Achievers · Accepted Answer

(3)

$x = 0 \Rightarrow Phase ϕ = 0 °$

$x = \frac{A}{\sqrt{2}} \Rightarrow Phase ϕ = \frac{π}{4}$

$∴$ $phase covered Δ ϕ = \frac{π}{4}$

$time t = \frac{Phase}{ω} = \frac{π}{4 ω} = \frac{π}{4} \times \frac{T}{2 π} = \frac{T}{8}$

$The time required by it to move from x = A to x = \frac{A}{\sqrt{2}},$

$t' = \frac{T}{4} - \frac{T}{8} = \frac{T}{8} = \frac{5}{8} s$

Solution

Q.
A particle is executing simple harmonic motion. Its amplitude is A and time period is 5 sec. The time required by it to move from $x = A$ to $x = \frac{A}{\sqrt{2}}$ is _________ sec. [2026]

1 $\frac{1}{4}$

2 $\frac{5}{4}$

3 $\frac{5}{8}$

4 $\frac{3}{8}$

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Solution

Q. A particle is executing simple harmonic motion. Its amplitude is A and time period is 5 sec. The time required by it to move from x=A to x=A2 is _________ sec. [2026]

1 14

2 54

3 58

4 38