Distinguish between forced vibrations and resonance. Draw neat, labelled diagrams for the modes of vibration of a streched string in second harmonic and third harmonic.
The area of the upper face of a rectangular block is `0.5mxx0.5m` and the lower face is fixed. The height of the block is `1cm`. A shearing force applied at the top face produces a displacement of `0.015 mm`. Find the strain and shearing force.
(Modulus of rigidity : `eta=4.5xx10^(10)N//m^(2)`)

Explanation

Forced vibrations: The vibrations of a body which take place under the unfluence of an external periodic force acting on it are called the forced vibrations.
Resonance : Resonance is a special case of forced vibrations. When the frequency of an externally applied periodic force on a body is equal to its natural frequency, the body readily begins to vibrate with an increased amplitude. This phenomenon is known as resonance. The vibrations of large amplitude are called resonant vibrations.

Numerical:
Given: `A=0.5mxx0.5m`
`h=1cm=1xx10^(-2)m`
`Deltax=0.015mm=0.015xx10^(-3)m`.
Shearing strain `=(Deltax)/(y)=(0.015xx10^(-3))/(1xx10^(-2))`
`=1.50xx10^(-3)`
Shearing stress `=etaxx`Shearing strain
`=4.5xx10^(10)xx1.50xx10^(-3)`
`=6.75xx10^(7) N//m^(2)`
Shearing force `=` Shearing stress `xxA`
`=6.75xx10^(7)xx0.5xx0.5`
`=1.69xx10^(7)N`