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A body is executing simple harmonic motion with an angular frequency 2 rad/s. The velocity of the body at 20 mm displacement, when the amplitude of motion is 60 mm, is
  • a)
    40 mm/s
  • b)
    60 mm/s
  • c)
    113 mm/s
  • d)
    120 mm/s
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A body is executing simple harmonic motion with an angular frequency 2...
Solution:

Given, angular frequency of simple harmonic motion, ω = 2 rad/s

Amplitude of motion, A = 60 mm

Displacement of body, x = 20 mm

Velocity of body, v = ?

Formula used:

The displacement of a body executing simple harmonic motion is given by,

x = A cos(ωt)

Differentiating both sides with respect to time, we get

v = -ωA sin(ωt)

where v is the velocity of the body.

Calculation:

Given, amplitude of motion, A = 60 mm

Displacement of body, x = 20 mm

We know that,

x = A cos(ωt)

cos(ωt) = x/A = 20/60 = 1/3

From the trigonometric ratios, we get,

sin(ωt) = √(1 - cos²(ωt))

= √(1 - (1/3)²)

= √(8/9)

= 2√2/3

Therefore,

v = -ωA sin(ωt)

= -2 × 60 × 2√2/3

= -240√2/3 mm/s

Taking the magnitude of velocity, we get

|v| = 240√2/3 mm/s

|v| ≈ 113 mm/s

Hence, the velocity of the body at 20 mm displacement, when the amplitude of motion is 60 mm, is 113 mm/s. Therefore, option (c) is correct.
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A body is executing simple harmonic motion with an angular frequency 2...
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A body is executing simple harmonic motion with an angular frequency 2 rad/s. The velocity of the body at 20 mm displacement, when the amplitude of motion is 60 mm, isa)40 mm/sb)60 mm/sc)113 mm/sd)120 mm/sCorrect answer is option 'C'. Can you explain this answer?
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