Question

# Figures given correspond to two circular motions. The radius of the circle, the period of revolution, the initial position, and the sense of revolution (i.e. clockwise or anti-clockwise) are indicated on each figure. Obtain the corresponding simple harmonic motions of the x-projection of the radius vector of the revolving particle P, in each case.

Open in App
Solution

## (a) Time period, t=2sAmplitude, A=3cmAt time, t=0, the radius vector OP makes an angle π/2 with the positive x-axis, i.e., phase angle ϕ=+π/2Therefore, the equation of simple harmonic motion for the x-projection of OP, at the time t, is given by the displacement equation:x=Acos[2πtT+ϕ] =3cos(2πt2+π2)=−3sin(2πt2)∴x=−3sin(πt)cm(b) Time Period, t=4sAmplitude, a=2mAt time t=0, OP makes an angle π with the x-axis, in the anticlockwise direction, Hence, phase angle ϕ=+πTherefore, the equation of simple harmonic motion for the x-projection of OP, at the time t, is given as:x=acos[2πtT+ϕ] =2cos(2πt4+π)∴x=−2cos(π2t)m

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Defining Hyperbola
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program