Question

Obtain the corresponding simple harmonic motions of the x-projection of the radius vector of the revolving particle P, in each case.

Answer 1

(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:

Answer 2

Answer:

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