Answer:
Explanation:
Given a mass spring system
At t = 0.1s, the positions is at x=8cm
x(0.1) = 8cm = 0.08m
Spring constant k=16N/m
Mass attached m = 4kg
Amplitude of oscialltion A=10cm = 0.1m
The angular frequency can be calculated using
w = √k/m
Where k is spring constant in N/m
m is mass attached object to the spring in kg
w = √16/4 = √4
w = 2rad/s.
Generally, the equation of a spring is given as
x = ACos(wt+Φ)
Where,
A is amplitude in metre
w is angular frequency in rad/sec
Φ is phase in radian
x(t) = 0.1Cos(2t + Φ)
At t=0.1 x = 0.08
0.08 = 0.1Cos(0.2+Φ)
Cos(0.2+Φ) = 0.08/0.1
Cos(0.2+Φ) = 0.8
0.2+Φ = ArcCos(0.8), note angle in radiant
0.2+Φ = 0.644
Φ = 0.644 — 0.2
Φ = 0.444 rad.
The phase of the SHM is 0.444rad
The answer is E = 0.44 rad
