An object in simple harmonic motion has period 14 pi At time

An object in simple harmonic motion has period 1/4 pi. At time t = 0, y(0) = 2, y\'(0) = 0. The equation of motion is: y = 2 sin (4t + 1/2 pi) y = 2 sin (8t + 1/2 pi) y = 4 sin (8t + 1/2 pi) y = sin (4t + 1/4 pi) None of the above.

Solution

plugging in individual values an checking the equation which satisfies ithe above given data we find that equation 2 is correct since

t = pi/4 we have to get y(0) =2

now ,

2sin(8*pi/4 + pi/2)

=> 2sin(5pi/2)

=> 2

hence equation 2 is correct