Simple harmonic motion question (1 Viewer)

ghostman_on_3rd · Jun 21, 2009

hi im having trouble with this question, i need help.

A point moves with SHM; if when at distances of 3 and 4cm from the centre of its path, its velocities are 8 and 6cm/s respectively, find its period and its acceleration when at its greatest distance from the centre.

thanks in advance</SPAN>

Drongoski · Jun 21, 2009

Not necessarily the best method.

$\80dpi v^{2}\ =\ n^{2}(a^{2}\ -\ x^{2})\ \ taking\ centre\ @\ x=0\\ \\ \therefore \ \ 8^{2}\ =\ n^{2}(a^{2}-3^{2})\ \ \Rightarrow \ \ n^{2}(a^{2}-9)\ =\ 64\\ \\ \ \ 6^{2}\ =\ n^{2}(a^{2}-4^{2})\ \ \Rightarrow \ \ n^{2}(a^{2}-16)\ =\ 36\\ \\ \therefore \ \ \frac{a^{2}-9}{a^{2}-16}\ =\ \frac{64}{36}\ =\ \frac{16}{9}\\ \\ Solving\ \Rightarrow \ a^{2}\ =\ 25\ \ \Rightarrow \ a=5\\ \\\therefore \ \ n^{2}(5^{2}-4^{2})\ =\ 36\ \ \Rightarrow \ \ n^{2}\ =\ 4\ \ \Rightarrow \ \ n\ =\ 2\\ \\ \therefore \ \ period\ =\ \frac{2\pi }{n}\ =\ \pi \ secs.\\ \\ Max\ acceleration\ =\ -n^{2}\times a\ =\ -4\times 5\ cm/sec^{2}\ \ =\ \ 20\ cm/sec^{2}\ \ towards\ the\ centre\$

ghostman_on_3rd · Jun 21, 2009

nice ! i understand, thanks man

Joel8945 · Jun 21, 2009

ghostman_on_3rd said:
hi im having trouble with this question, i need help.

A point moves with SHM; if when at distances of 3 and 4cm from the centre of its path, its velocities are 8 and 6cm/s respectively, find its period and its acceleration when at its greatest distance from the centre.

thanks in advance</SPAN>

E = 0.5(m*v^2 + kx^2)

E = 0.5(0.0064m + 0.0009k)
E = 0.5(0.0036m + 0.0016k)

0.0064m + 0.0009k = 0.0036m + 0.0016k

0.0007k = 0.0028m

k = 4m

ω = 2π/T (T = period)

ω = sqrt(k/m) = sqrt(4m/m) = 2

2 = 2π/T => T = π

The period is π seconds.

When its at its greatest distance from the centre:

E = 0.5kx^2

4m*x^2 = 0.0036m + 0.0016*4m

4mx^2 = 0.01m

x^2 = 0.0025

x = 0.05m

a(t) = -ω^2*x(t) = -4*0.05 = -4*0.05 = -0.2m/s^2

so the acceleration at its farthest point from the centre is -20cm/s^2 and the period is constant throughout the SHM which was determined to be approximately 3.14s.

tommykins · Jun 21, 2009

rofl yeah use physics methods righto.

ignore the above post guys.

Simple harmonic motion question (1 Viewer)

ghostman_on_3rd

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Drongoski

Well-Known Member

ghostman_on_3rd

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Joel8945

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tommykins

i am number -e^i*pi

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