Exercise · ZW-HARMONIC-OSCILLATOR-004 · ★☆☆ Basic
Solve \(y''+25y=0\), \(y(0)=2\), \(y'(0)=0\).
Choose one option.
Show answer
- D. \(y=2\cos5t\)
Explanation
With \(\omega=5\), \(y=c_1\cos5t+c_2\sin5t\). \(y(0)=2\) gives \(c_1=2\) and \(y'(0)=5c_2=0\) gives \(c_2=0\).
Review the concept: Harmonic oscillator
Model of a mass \(m\) attached to a spring of constant \(k\), with no friction or external force, whose position \(y(t)\) oscillates with angular frequency \(\omega\) about equilibrium.
\[my''+ky=0,\qquad \omega=\sqrt{k/m}\]
More practice problems: harmonic oscillator
- ZW-HARMONIC-OSCILLATOR-001 A mass m=1 attached to a spring with k=9 satisfies my''+ky=0. Find the angular frequency ω.
- ZW-HARMONIC-OSCILLATOR-002 For 4y''+16y=0, what is the angular frequency ω?
- ZW-HARMONIC-OSCILLATOR-003 A mass m=1 on a spring with k=4 oscillates without damping. What is the period T?
- ZW-HARMONIC-OSCILLATOR-005 Solve y''+4y=0, y(0)=0, y'(0)=6.
- ZW-HARMONIC-OSCILLATOR-006 An oscillator moves as y=3cos 2t+4sin 2t. What is its amplitude?
- ZW-HARMONIC-OSCILLATOR-007 A mass m=2 on a spring with k=8 starts with y(0)=1, y'(0)=4. What is the amplitude?
- ZW-HARMONIC-OSCILLATOR-008 The spring is replaced by one with k four times larger, with the same m. What happens to the angula…
- ZW-HARMONIC-OSCILLATOR-009 Two oscillators have the same m and k but are released with different initial conditions. What is t…