26. We saw in Section 11.6 that a pendulum formed by a bob of mass m...
26. We saw in Section 11.6 that a pendulum formed by a bob of mass m on the end of a massless string of length L is a harmonic oscillator, in the limit of small oscillations. Let us use an angle to locate the position of the pendulum bob, as shown in figure 11.6 and let us use w for the angular speed of the pendulum. Consider the variables m, g, L, θ, and w and find an expression for the total energy of a pendulum in the limit of small oscillations.
Homework Answers
Total energy of pendulum = potential energy at extreme position,
= mg *(L - L cos theta)
= mgL*(1 - cos theta)
= mgL*( 1 - (1 - θ^2/2)). as for small θ, cos θ = 1 -θ^2/2
= mgL*θ^2/4 answer
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