Obtain the corresponding simple harmonic motions of the x-projection of the radius vector of the revolving particle P, in each case.
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(a) Time period, t = 2 s
Amplitude, A = 3 cm
At time, t = 0, the radius vector OP makes an angle π/2 with the positive x-axis,.e., phase angle Φ = +π/2
Therefore, the equation of simple harmonic motion for the x-projection of OP, at the time t, is given by the displacement equation:
(b) Time Period, t = 4 s
Amplitude, a = 2 m
At time t = 0, OP makes an angle π with the x-axis, in the anticlockwise direction, Hence, phase angle Φ = +π
Therefore, the equation of simple harmonic motion for the x-projection of OP, at the time t, is given as:
Amplitude, A = 3 cm
At time, t = 0, the radius vector OP makes an angle π/2 with the positive x-axis,.e., phase angle Φ = +π/2
Therefore, the equation of simple harmonic motion for the x-projection of OP, at the time t, is given by the displacement equation:
(b) Time Period, t = 4 s
Amplitude, a = 2 m
At time t = 0, OP makes an angle π with the x-axis, in the anticlockwise direction, Hence, phase angle Φ = +π
Therefore, the equation of simple harmonic motion for the x-projection of OP, at the time t, is given as:
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ANSWER
(a) Time period, t=2s
Amplitude, A=3cm
At time, t=0, the radius vector OP makes an angle π/2 with the positive x-axis, i.e., phase angle ϕ=+π/2
Therefore, the equation of simple harmonic motion for the x-projection of OP, at the time t, is given by the displacement equation:
x=Acos[
T
2πt
+ϕ]
=3cos(
2
2πt
+
2
π
)=−3sin(
2
2πt
)
∴x=−3sin(πt)cm
(b) Time Period, t=4s
Amplitude, a=2m
At time t=0, OP makes an angle π with the x-axis, in the anticlockwise direction, Hence, phase angle ϕ=+π
Therefore, the equation of simple harmonic motion for the x-projection of OP, at the time t, is given as:
x=acos[
T
2πt
+ϕ]
=2cos(
4
2πt
+π)
∴x=−2cos(
2
π
t)m
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