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The instantaneous displacement of a simple harmonic oscillator is given by y = A cos (ωt + n/4). Its speed will be maximum at the time:). Its speed will be maximum at the time:
- a)n/4ω
- b)ω/n
- c)ω/2n
- d)2n/ω
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The instantaneous displacement of a simple harmonic oscillator is give...
The instantaneous displacement of a simple pendulum oscillator is given as y = acos(ωt + π/4)
differentiating with respect to time,
dy/dt = -ωasin(ωt + π/4)
here, dy/dt is the velocity of a particle executing SHM.
so, speed of particle = | dy/dt | = ωasin(ωt + π/4)
so, dy/dt will be maximum when sin(ωt + π/4) will be maximum i.e., 1
so, sin(ωt + π/4) = 1 = sin(π/2)
⇒ωt + π/4 = π/2
⇒ωt = π/4
⇒t = π/(4ω)
hence, at t = π/(4ω) , speed of the particle will be maximum.
differentiating with respect to time,
dy/dt = -ωasin(ωt + π/4)
here, dy/dt is the velocity of a particle executing SHM.
so, speed of particle = | dy/dt | = ωasin(ωt + π/4)
so, dy/dt will be maximum when sin(ωt + π/4) will be maximum i.e., 1
so, sin(ωt + π/4) = 1 = sin(π/2)
⇒ωt + π/4 = π/2
⇒ωt = π/4
⇒t = π/(4ω)
hence, at t = π/(4ω) , speed of the particle will be maximum.
Most Upvoted Answer
The instantaneous displacement of a simple harmonic oscillator is give...
Explanation:
The equation of motion for a simple harmonic oscillator is given by y = A cos (ωt + φ), where A is the amplitude, ω is the angular frequency, t is the time, and φ is the phase angle. The speed of the oscillator is the time derivative of the displacement, dy/dt = -Aω sin (ωt + φ).
To find the time when the speed is maximum, we need to find the time when the sine function has its maximum value. The maximum value of the sine function is 1, which occurs when the argument is π/2 or 3π/2. In this case, the argument of the sine function is ωt + φ = nπ/2, where n is an integer.
Since the displacement is given by y = A cos (ωt + φ), we can write ωt + φ = nπ/2 + π/2, which gives us the time when the speed is maximum as t = (n/4)π.
Therefore, the correct option is A. The speed of the oscillator will be maximum at the time t = (n/4)π.
The equation of motion for a simple harmonic oscillator is given by y = A cos (ωt + φ), where A is the amplitude, ω is the angular frequency, t is the time, and φ is the phase angle. The speed of the oscillator is the time derivative of the displacement, dy/dt = -Aω sin (ωt + φ).
To find the time when the speed is maximum, we need to find the time when the sine function has its maximum value. The maximum value of the sine function is 1, which occurs when the argument is π/2 or 3π/2. In this case, the argument of the sine function is ωt + φ = nπ/2, where n is an integer.
Since the displacement is given by y = A cos (ωt + φ), we can write ωt + φ = nπ/2 + π/2, which gives us the time when the speed is maximum as t = (n/4)π.
Therefore, the correct option is A. The speed of the oscillator will be maximum at the time t = (n/4)π.
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Community Answer
The instantaneous displacement of a simple harmonic oscillator is give...
The instantaneous displacement of a simple pendulum oscillator is given as y = acos(ωt + π/4)
differentiating with respect to time,
dy/dt = -ωasin(ωt + π/4)
here, dy/dt is the velocity of particle executing SHM.
so, speed of particle = | dy/dt | = ωasin(ωt + π/4)
so, dy/dt will be maximum when sin(ωt + π/4) will be maximum i.e., 1
so, sin(ωt + π/4) = 1 = sin(π/2)
⇒ωt + π/4 = π/2
⇒ωt = π/4
⇒t = π/(4ω)
hence, at t = π/(4ω) , speed of particle will be maximum.
differentiating with respect to time,
dy/dt = -ωasin(ωt + π/4)
here, dy/dt is the velocity of particle executing SHM.
so, speed of particle = | dy/dt | = ωasin(ωt + π/4)
so, dy/dt will be maximum when sin(ωt + π/4) will be maximum i.e., 1
so, sin(ωt + π/4) = 1 = sin(π/2)
⇒ωt + π/4 = π/2
⇒ωt = π/4
⇒t = π/(4ω)
hence, at t = π/(4ω) , speed of particle will be maximum.
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The instantaneous displacement of a simple harmonic oscillator is given by y = A cos (ωt + n/4). Its speed will be maximum at the time:). Its speed will be maximum at the time:a)n/4ωb)ω/nc)ω/2nd)2n/ωCorrect answer is option 'A'. Can you explain this answer?
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