Question

7. An object attached with a spring undergoes simple harmonic motion, represented by the displacement = (1.0m) Cos (1.5m t) . Compare with the standard equation for simple harmonic equation: x = A cos (w t). (i) Find the amplitude of oscillation? ute ew m .s (ii) Calculate the displacement x at t 0, 1, 2, 3, 4 and 5 seconds and filled the table below (calculator should be in radian mode for finding x values ) Displacement x (m) Time t (s) 1 2 3 5 time graph of the oscillatory motion on the following graph. (iii) Draw the displacement x (m) t (s) 3

Answer 1

Displacement equation of object is given as : * Elim) Cas(is tt) Standerd equation for simple harmonic equation x= A Costot) comparing both equations, .. we get A=1m () so, amplitude of oscination is equal to im. (1) displacements at t= 0,112, 3, 4 and 5 seconds. at t=0 see. x= 1 cos (1.5 txo) Tse im - at t= I see to I Cod (1-5 TT. 1) = cos () = 0 [pezo) when trisee at t=2 see de El cos (15 97.2) = cos (2")=-1

at t=3 see se el cos (151.3) a cas(4:57) 20 at t=4 sec x=1 cas (157.4) = cas (67) al le=1 at t=s see Bez 1 Cod (15 TT-5) =0 Trezo) Now, Table Temel sed displacement se (m)

alisplacement - time, graph- (111 Am) भजन । 2 t(set) /3 4 -1 + - - - - . . . . . . . .