a mass on a spring vibrates in simple harmonic motion at afrequency of 1 Hz and

Question

a mass on a spring vibrates in simple harmonic motion at afrequency of 1 Hz and amplitude of 4.0 cm. if a timeris started when its displacement is a maximum (hence x=4cm @ t= 0)what is : a) the position of the mass when t= 2.25s? b) the speed of the mass when t= 2.25s? c) the acceleration of the mass when t= 2.25s? a mass on a spring vibrates in simple harmonic motion at afrequency of 1 Hz and amplitude of 4.0 cm. if a timeris started when its displacement is a maximum (hence x=4cm @ t= 0)what is : a) the position of the mass when t= 2.25s? b) the speed of the mass when t= 2.25s? c) the acceleration of the mass when t= 2.25s?

Explanation / Answer

frequency f = 1 Hz angular frequency w = 2 f = 6.28 hz amplitude A = 4 cm we know displacement at time t is x =A cos w t                                                          ( 4 cm ) cos ( 6.28 t ) (a). position at time t= 2.25 is x = ( 4cm ) cos ( 6.28 * 2.25 )                                                  = 0 cm (b). velocity v = dx / dt                      = A w [ -sin wt ] So, velocity at t= 2.25 s is   v =-25.13 cm / s (c), accleration a = d v / dt                            = - Aw ^ 2 cos wt accleration at t= 2.25 s is   a = 0 cm /s^2                            

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