Question

• Consider a pendulum made of a spring with a mass m on the end (see diagram below). The spring is arranged to lie in a straight line (which we can arrange by, say, wrapping the spring around a rigid massless rod). The equilibrium length of the spring is $\ell$. Let the spring have length $\ell + x(t)$, and let its angle with the vertical be $\theta(t)$. Assuming that the motion takes place in a vertical plane, find the equations of motion for x and $\theta$.

Name: • Consider a pendulum made of a spring with a mass m on the end (see diagram below). The spring is arranged to lie in a straight line (which we can arrange by, say, wrapping the spring around a rigid massless rod). The equilibrium length of the spring is ℓ. Let the spring have length ℓ + x(t), and let its angle with the vertical be θ(t). Assuming that the motion takes place in a vertical plane, find the equations of motion for x and θ.
Uploaded: 2023-05-19T16:17:38-08:00
Duration: 3 min 58 s
Channel: Sam Stansfield

          • Consider a pendulum made of a spring with a mass m on the end (see diagram below). The spring is arranged to lie in a straight line (which we can arrange by, say, wrapping the spring around a rigid massless rod). The equilibrium length of the spring is $\ell$. Let the spring have length $\ell + x(t)$, and let its angle with the vertical be $\theta(t)$. Assuming that the motion takes place in a vertical plane, find the equations of motion for x and $\theta$.

• Consider a pendulum made of a spring with a mass m on the end (see diagram below). The spring is arranged to lie in a straight line (which we can arrange by, say, wrapping the spring around a rigid massless rod). The equilibrium length of the spring is ℓ. Let the spring have length ℓ + x(t), and let its angle with the vertical be θ(t). Assuming that the motion takes place in a vertical plane, find the equations of motion for x and θ.

Added by Enrique M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sam Stansfield

05/19/2023

Step 1

There are three forces acting on the mass: gravity (mg downward), the spring force (along the spring), and any constraint forces that keep the motion in the vertical plane. Show more…

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Consider a pendulum made of a spring with a mass m on the end (see diagram below). The spring is arranged to lie in a straight line (which we can arrange by, say, wrapping the spring around a rigid massless rod). The equilibrium length of the spring is l. Let the spring have length l+x(t), and let its angle with the vertical be heta (t). Assuming that the motion takes place in a vertical plane, find the equations of motion for x and heta . Consider a pendulum made of a spring with a mass m on the end(see diagram below). The spring is arranged to lie in a straight line (which we can arrange by, say, wrapping the spring around a rigid massless rod).The equilibrium length of the spring is e. Let the spring have length + x(t), and let its angle with the vertical be 0(t). Assuming that the motion takes place in a vertical plane, find the equations of motion for x and e.