A simple harmonic oscillator has amplitude 10 cm and it completes 120 oscillations in 60 Seconds if the initial phase is pi by 2 write expressions for its displacement and velocity
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Hey dear,
● Answer -
x = -10sin(4πt) cm
v = -40πcos(4πt) cm/s
● Explaination -
# Given -
A = 10 cm
f = 120/60 = 2 Hz
θ = π/2 rad
# Solution -
Angular velocity of SHM is -
ω = 2πf
ω = 2π×2
ω = 4π rad/s
Displacement of particle in SHM is given by -
x = A.cos(ωt+θ)
x = 10cos(4πt+π/2)
x = -10sin(4πt) cm
Velocity of particle in SHM is given by -
v = Aω.sin(ωt+θ)
v = 10×4πsin(4πt+π/2)
v = -40πcos(4πt) cm/s
Hope this helped you...
● Answer -
x = -10sin(4πt) cm
v = -40πcos(4πt) cm/s
● Explaination -
# Given -
A = 10 cm
f = 120/60 = 2 Hz
θ = π/2 rad
# Solution -
Angular velocity of SHM is -
ω = 2πf
ω = 2π×2
ω = 4π rad/s
Displacement of particle in SHM is given by -
x = A.cos(ωt+θ)
x = 10cos(4πt+π/2)
x = -10sin(4πt) cm
Velocity of particle in SHM is given by -
v = Aω.sin(ωt+θ)
v = 10×4πsin(4πt+π/2)
v = -40πcos(4πt) cm/s
Hope this helped you...
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