A frictionless piston of mass 0.20 kg and area 0.01 m² encloses a gas at equilibrium pressure 10⁵ Pa and volume 0.01 m³. Small oscillations are rapid and adiabatic with γ = 1.4. If ω² = N s⁻², find N.
Physics · Simple Harmonic Motion · time period of linear shm
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Question

A frictionless piston of mass 0.20 kg and area 0.01 m² encloses a gas at equilibrium pressure 10⁵ Pa and volume 0.01 m³. Small oscillations are rapid and adiabatic with γ = 1.4. If ω² = N s⁻², find N.

Physics · Simple Harmonic Motion · time period of linear shm

G1 Physics · Accepted Answer

For the gas-piston oscillator, ω² = γPA²/(mV). Substitute γ = 1.4, P = 10⁵ Pa, A = 0.01 m², m = 0.20 kg, V = 0.01 m³. Now, A² = 10⁻⁴ m⁴. Thus, ω² = 1.4×10⁵×10⁻⁴/ (0.20×0.01) = 14/0.002 = 7000 s⁻². Hence, N = 7000.