Question

A 200g mass oscillates with a displacement given by x(t)=(7.0 cm) cos[(5/s)t+2pi/9] Find the

A. Angular frequency

B. Frequency

C.Period

D.Spring constant

E. Maximum speed

F. maximum acceleration

g. acceleratiom when the speed is equal to the maximum speed

h. phase when t=2s

I. displacment when t=2s

J. velocity when t=2s

k. acceleration when t=2s

Answer 1

Given

x(t)=(7.0 cm) cos[(5/s)t+2pi/9]

The equation is similiar to

x(t)=(A cm) cos[(W)t+Φ ]

a)

ANgular frequency = 5/s

b)

Frequency ,f = W/2pi = 5/s * 1/2pi = 5/2*pi*s

c)

Period, T = 1/f = 2*pi*s/5

d)

we have , W = sqrt (K/m)

K = m*W^2

K , Spring Constant = 0.2 * (5/s)^2 = 5/s^2

e)

Maximum speed = v = A*W = (0.07 *5/s) m/second

f)

Maximum acceleration ,a = A*W^2 = 0.07*(5/s)^2 m/second^2

h)

phase = 2*pi/9

i)

displacement,x = 0.07* cos (10/s + 2*pi/9)

j)

velocity = dx/dt = - 0.07*5/s * sin (10/s +2*pi/9)

k)

acceleration = dv/dt = -0.07*25/s^2 cos (10/s +2*pi/9)