A block of mass oscillates on a frictionless horizontal spring with amplitude while…

PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Plasma Physics · The plasma state and single-particle motion

Plasma Physics, Ch Slow changes and what survives them: adiabatic invariants, mirrors and trapped orbits

Problem

A block of mass

m = 0.20\,\mathrm{kg}

oscillates on a frictionless horizontal spring with amplitude

3.0\,\mathrm{cm}

while the spring constant is

k_1 = 50\,\mathrm{N\,m^{-1}}

. Over many oscillation periods an external agent slowly increases the spring constant to

k_2 = 200\,\mathrm{N\,m^{-1}}

, four times its original value, without otherwise disturbing the motion. ((a)) Find the new angular frequency

\omega_2

. ((b)) Find the ratio

E_2/E_1

of the new oscillation energy to the old. ((c)) Find the new amplitude.