Question

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.

Answer 1

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 2

Answer:

• The Time period (T) of the oscillation is  π sec.

Given:

1. Mass of the body (M) = 2 Kg.
2. Relation; F + 8 x = 0

Explanation:

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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.

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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.

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