SHMEasy
Question
The motion of a particle executing simple harmonic motion is described by the displacement function,
x(t) = A cos (ωt + φ).
If the initial (t = 0) position of the particle is 1 cm and its initial velocity is ω cm/s, then its equation is The angular frequency of the particle is π s-1.
x(t) = A cos (ωt + φ).
If the initial (t = 0) position of the particle is 1 cm and its initial velocity is ω cm/s, then its equation is The angular frequency of the particle is π s-1.
Options
A.√2 cos 
B.√2 cos 
C.2 cos 
D.2 cos 
Solution
x = Acos (ωt + φ)
1 = A cos φ .....(1)
v = - Aω sin (ωt + θ)
π = - A ω sin θ
- 1 = A sin π ....(2)
from (1) & (2)
A = √2
tan φ = - 1
∴ φ will be -
1 = A cos φ .....(1)
v = - Aω sin (ωt + θ)
π = - A ω sin θ
- 1 = A sin π ....(2)
from (1) & (2)
A = √2
tan φ = - 1
∴ φ will be -
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