Name: Velocity and Acceleration in SHM
Uploaded: 2019-07-19
Duration: 5 min 47 s
Description: In this video, we will derive the equations and graphs of the velocity and acceleration of an object in SHM. Let us watch this video now.

Question

Suppose that a simple pendulum consists of a small $60.0 g$ bob at the end of a cord of negligible mass. If the angle $θ$ between the cord and the vertical is given by

$θ = (0 .0800 rad) \cos [(6 .80 rad s^{- 1}) t + ϕ]$ , what are (a) the pendulum's length and (b) its maximum kinetic energy?

Accepted Answer

Given:
The angular displacement-time equation of the pendulum is,
$θ = (0 .0800 rad) \cos [(6 .80 rad s^{- 1}) t + ϕ] . . . (1)$ .

(a) Comparing equation (1) with the standard form, we get that, the angular frequency $ω = 6.80 rad s^{- 1}$ . Again we know for a pendulum,
$ω = \sqrt{\frac{g}{L}}$
where, $L$ is the pendulum's length.
Substituting the values we get,
$L = \frac{9.8}{{(6.8)}^{2}}$
$\Rightarrow L = 0.212 m = 21.2 cm$ .

(b) From equation (1) we also get that the amplitude of oscillation is, $A = 0.08 \times L = 0.017 m$ .
Hence, the maximum kinetic energy is given by,
$K_{\max} = \frac{1}{2} m ω^{2} A^{2}$
$= \frac{1}{2} \times 60 \times 10^{- 3} \times {(6.8)}^{2} \times {(0.017)}^{2} = 4.01 \times 10^{- 4} J$ .

Suppose that a simple pendulum consists of a small $60.0 g$ bob at the end of a cord of negligible mass. If the angle $θ$ between the cord and the vertical is given by

$θ = (0 .0800 rad) \cos [(6 .80 rad s^{- 1}) t + ϕ]$ , what are (a) the pendulum's length and (b) its maximum kinetic energy?

Important Questions on Oscillations

Learn and Prepare for any exam you want !

Suppose that a simple pendulum consists of a small 60.0 g bob at the end of a cord of negligible mass. If the angle θ between the cord and the vertical is given by θ=0.0800radcos6.80rad s-1t+ϕ, what are (a) the pendulum's length and (b) its maximum kinetic energy?

Important Questions on Oscillations

Learn and Prepare for any exam you want !

Suppose that a simple pendulum consists of a small $60.0 g$ bob at the end of a cord of negligible mass. If the angle $θ$ between the cord and the vertical is given by

$θ = (0 .0800 rad) \cos [(6 .80 rad s^{- 1}) t + ϕ]$ , what are (a) the pendulum's length and (b) its maximum kinetic energy?