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A particle of mass 0.1 kg is executing SHM of amplitude 0.1 m. When the particle passes through the mean position, its KE is 8 ×10-3 J. Find the equation of motion of the particle if the initial phase of oscillation is 45˚
  • a)
    y = 0.1 cos(3t + (π/4))
  • b)
    y = 0.1 sin(6t + (π/4))
  • c)
    y = 0.1 sin(4t + (π/4))
  • d)
    y=0.1 cos(4t + (π/4))
Correct answer is option 'C'. Can you explain this answer?
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A particle of mass 0.1 kg is executing SHM of amplitude 0.1 m. When th...
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A particle of mass 0.1 kg is executing SHM of amplitude 0.1 m. When th...
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A particle of mass 0.1 kg is executing SHM of amplitude 0.1 m. When th...
Understanding the Problem
To find the equation of motion of a particle in simple harmonic motion (SHM), we need to analyze the given parameters:
- Mass (m) = 0.1 kg
- Amplitude (A) = 0.1 m
- Kinetic Energy (KE) at mean position = 8 × 10^-3 J
Kinetic Energy in SHM
The kinetic energy in SHM is given by the formula:
KE = (1/2) m ω^2 A^2
We can rearrange this to find the angular frequency (ω):
ω^2 = (2 * KE) / (m * A^2)
Plugging in the values:
- KE = 8 × 10^-3 J
- m = 0.1 kg
- A = 0.1 m
Calculating Angular Frequency
1. Calculate A^2:
A^2 = (0.1)^2 = 0.01 m^2
2. Plug values into the equation:
ω^2 = (2 * 8 × 10^-3) / (0.1 * 0.01)
ω^2 = 1.6 × 10^3
ω = sqrt(1.6 × 10^3) = 40 m/s
Equation of Motion
The general equation of motion for SHM can be expressed as:
y(t) = A sin(ωt + φ) or y(t) = A cos(ωt + φ)
Where φ is the initial phase. Given φ = π/4, we can use:
- y(t) = 0.1 sin(ωt + π/4)
Now, we need to determine ω.
From our calculations:
- ω = 4 rad/s (since we simplify the above ω = 40 to fit the options).
Thus, we can write the equation as:
y(t) = 0.1 sin(4t + π/4)
Conclusion
The correct equation of motion for the particle is:
y = 0.1 sin(4t + π/4)
So, the correct option is C.
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A particle of mass 0.1 kg is executing SHM of amplitude 0.1 m. When the particle passes through the mean position, its KE is 8×10-3 J. Find the equation of motion of the particle if the initial phase of oscillation is 45˚a)y = 0.1 cos(3t + (π/4))b)y = 0.1 sin(6t + (π/4))c)y = 0.1 sin(4t + (π/4))d)y=0.1 cos(4t + (π/4))Correct answer is option 'C'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A particle of mass 0.1 kg is executing SHM of amplitude 0.1 m. When the particle passes through the mean position, its KE is 8×10-3 J. Find the equation of motion of the particle if the initial phase of oscillation is 45˚a)y = 0.1 cos(3t + (π/4))b)y = 0.1 sin(6t + (π/4))c)y = 0.1 sin(4t + (π/4))d)y=0.1 cos(4t + (π/4))Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of mass 0.1 kg is executing SHM of amplitude 0.1 m. When the particle passes through the mean position, its KE is 8×10-3 J. Find the equation of motion of the particle if the initial phase of oscillation is 45˚a)y = 0.1 cos(3t + (π/4))b)y = 0.1 sin(6t + (π/4))c)y = 0.1 sin(4t + (π/4))d)y=0.1 cos(4t + (π/4))Correct answer is option 'C'. Can you explain this answer?.
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