Grade upto college level Mechanics

A point mass m is suspended at the end of a mass less wire of length l and cross section A. If Y is the Young’s modulus for the wire, obtain the frequency of oscillation for the simple harmonic motion along the vertical line.

Amit Saxena

12 Years agoGrade upto college level

1 Answer

Navjyot Kalra

12 Years ago

From fig. (b), due to equilibrium

T = mg ….(i)

But Y = T /A /ℓ / L

⇒ T = YA ℓ / L

From (i) and (ii)

mg = YA ℓ / L (iii)

From fig. (c)

Restoring force

= - [T - mg] = - [YA (ℓ + x ) / L - YA ℓ / L] [from (iii)]

= - YAx /L

On comparing this equation with F = - mω2x, we get

mω2 = YA / L

⇒ ω = √ YA / mL ⇒ 2π / T = √YA / mL

Frequency f = 1 / T = 1 / 2π √ YA / mL

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A point mass m is suspended at the end of a mass less wire of length l and cross section A. If Y is the Young’s modulus for the wire, obtain the frequency of oscillation for the simple harmonic motion along the vertical line.

Amit Saxena

1 Answer

Navjyot Kalra

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