Question

If the object-spring system is described by x = (0.310 m) cos (1.55t), find the following.

(a) the amplitude, the angular frequency, the frequency, and the period

A =	m
ω =	The angular frequency is ω in Acosωt. rad/s
f =	Hz
T =	s

(b) the maximum magnitudes of the velocity and the acceleration

vmax =	m/s
amax =	m/s2

(c) the position, velocity, and acceleration when t = 0.250 s

x =	m
v =	m/s
a =	m/s2

Answer 1

a)

x = (0.310 m) cos (1.55t)

general equation is given as

x = A Coswt

hence comparing the equation ,

A = Amplitude = 0.31 m

w = 1.55 rad/s

f = w/2 = 1.55/(2 x 3.14) = 0.25 Hz

T = time period = 1/f = 1/0.25 = 4 sec

b)

V_max = Aw = 0.310 x 1.55 = 0.48 m/s

a_max = A w² = 0.310 x 1.55² = 0.75 m/s²

c)

position at t = 0.25 sec is given as

x = (0.310) cos (1.55 x 0.25)

velocity equation is given as

v = dx/dt = - (0.310) (1.55) Sin (1.55 t)

at t = 0.25 sec

v = - (0.310) (1.55) Sin (1.55 x 0.25) = - 0.18 m/s

acceleration equation is given as

a = dv/dt = - (0.310) (1.55)² Cos (1.55 t)

a = - (0.310) (1.55)² Cos (1.55 x 0.25)

a = - 0.69