Question

An object is in simple harmonic motion. Find an equation for the motion given that the frequency is ¹⁄_π and at time t = 0, y = 1, and y' = 0. What is the equation of motion?

Answer 1

Write the general form of the SHM equation. y = A sin(at+0) (1) Here, y is the equation of motion. A is the amplitude of wave, o is the angular frequency, t is the time and is the phase angle. Given that, Radial frequency. f = Hz Angular frequency can be written as, 0 = 2nf = 2 Hz Substitute 2 Hz for o in the equation (1). y = Asin(2t+0) Now, substitute 0 for t and 1 for y in the above equation. 1= Asin (0) Now, differentiate equation (2) with respect to phase angle. y'= 2.Acos(2t+0)

Now, substitute 0 for t and 0 for y' in the above equation. 0 = 2.Acos(0) The value of cos is given by. cos(m) = cos() Substitute for “ in the equation (3). 1= A(1) 1= A Substitute 1 for A, for 0 and 2 Hz for w in the equation (2). Hence, the equation of motion for SHM is y = sin 21