2. Derive the equation of motion for the system shown. The oscillation is defined by the displacement $x$ measured from the equilibrium position of the block. The pulley's moment of inertia about its pinned center is $J$. Determine the natural frequency and damping ratio of the system. Ans: $\zeta = \frac{25c}{12\sqrt{k(m + J/(9r^2))}}$
Added by Iker P.
Close
Step 1
Sure! Let's break down the problem into smaller steps to solve it more easily. Show more…
Show all steps
Your feedback will help us improve your experience
Ravindra Samadiya and 81 other Physics 101 Mechanics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Presents a model for solving this problem. A vertical spring (spring constant $=112 \mathrm{~N} / \mathrm{m}$ ) is mounted on the floor, A $0.400-\mathrm{kg}$ block is placed on top of the spring and pushed down to start it oscillating in simple harmonic motion. The block is not attached to the spring. (a) Obtain the frequency (in $\mathrm{Hz}$ ) of the motion. (b) Determine the amplitude at which the block will lose contact with the spring.
A simple harmonic oscillator is created by attaching a spring with a spring constant of 541 J/m², to two blocks as shown in the figure. The mass of block A is 2 kg, the mass of block B is 6 kg, the mass of the pulley is 4 kg, θA = 24°, and θB = 27°. The pulley can be modelled as a uniformly dense solid cylinder rotating around an axis through its center. All surfaces are frictionless, the pulley is frictionless, and the rope passes over the pulley without slipping. What is the period (in s) of oscillations of this system?
Penny R.
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Watch the video solution with this free unlock.
EMAIL
PASSWORD