F - x equation of a body of mass 2kg in SHM is F + 8x = 0 Here, F is in newton and x in meter.Find time period of oscillations.
Answers
It is given that for SIMPLE HARMONIC MOTION , F-x equation is ,
F + 8x = 0
.) Now we have to find the time period (t) for the Simple Harmonic Motion.
.) Now , we have F + 8x = 0
=> F = -8x ... (1)
•) Now comparing (1) with F = -kx
Where , k is the spring constant , F is the force and x is the displacement , we get k = 8
•) Now , we know that ,
w = √ ( k / m) , where w is angular frequency , k is the spring constant and m is the mass .
•) Also , w = 2π / t where t is the time period .
Now , w = √( 8 / 2 )
=> w = √4 = 2
Now, 2π/t = 2
=> t = π = 3.14 sec
Answer:
- The Time period (T) of the oscillation is π sec.
Given:
- Mass of the body (M) = 2 Kg.
- Relation; F + 8 x = 0
Explanation:
____________________
From the given relation we know,
⇒ F + 8 x = 0
Simplifying,
⇒ F = - 8 x
⇒ - K x = - 8 x ∵ [ F = - K x ]
⇒ K x = 8 x
⇒ K = 8
⇒ K = 8 N/m
∴ We got the Force Constant.
____________________
____________________
From the relation we know,
⇒ T = 2 π √( m / K )
Substituting the values,
⇒ T = 2 π √( 2 / 8 )
⇒ T = 2 π √( 1 / 4 )
⇒ T = 2 π × 1 / 2
⇒ T = π
⇒ T = π Sec.
∴ The Time period (T) of the oscillation is π sec.
Note:
- Symbols have their usual meanings.
____________________