Simple Harmonic motion 25C(Fitzpatrick) (1 Viewer)

Shikobe · Apr 30, 2010

9. A particle executes SHM. When it is 2cm from its equilibrium position its velocity is 6cm/s: when it is 3cm, its velocity is 4cm/s. Find the period of its motion and the amplitude.

10. If x=asin(nt) + bcos(nt) find the velocity and acceleration of a particle whose displacement from a fixed point O is x at time t. Show that a=-n^2x and find the amplitude and maximum speed.

Drongoski · Apr 30, 2010

Q9 (SHM)

$v^{2}\ =\ n^{2}(a^{2}-x^{2})\ \ \ \ taking \ centre\ at\ origin\\ \\ \therefore \ \ \ 6^{2} \ =\ n^{2}(a^{2}-2^{2})\ \ =\ \ n^{2}a^{2}-4n^{2}\\ \\ and \ \ 4^{2}\ =\ n^{2}(a^{2}-3^{2})\ =\ n^{2}a^{2}-9n^{2}\\ \\ \therefore\ \ \ 5n^{2}\ =\ 20\ \ \Rightarrow \ \ n\ =\ 2 \ \ and\ \ a\ =\ \sqrt{13}\ cm\ \ \ =\ \ amplitude\\ \\ \therefore \ \ \ period\ \ T\ =\ \frac{2\pi }{n}\ \ =\ \ \frac{2\pi }{2}\ \ =\ \ \pi \ sec.$

Shikobe · Apr 30, 2010

Thankyou

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Simple Harmonic motion 25C(Fitzpatrick) (1 Viewer)

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