A rod with a mass of m = 20 kg and length l = 1 m hangs at rest when the force F = 189 N is applied. Find the angular velocity of the rod when it has rotated 90◦ clockwise. ω = number (2 significant figures) rad/s
Describe the oscillation (complete an expression x(t) for that oscillation). An object being displaced on the frictionless table to the left from equilibrium position at distance 0.3 m while it moving to the left with a speed 0.6 m/s. Coefficient of spring 100 N/m, and mass of the block 50 g. Draw a diagram and complete all calculations: A) Calculate the amplitude of the oscillation B) What is the initial Phase of this oscillation C) What is the angular frequency D) Write the equation x(t) E) Evaluate your answers using a unit circle. Evaluate your solutions by drawing a unit circle diagram.
An 8kg disc rotates without any friction about O. Determine the natural frequency in hertz of the disc. Assume there is no slipping between the disc and the cord around it during oscillation.
A ring of mass m slides over a rod with mass M and length L, which is pivoted at one end and hangs vertically. The mass m is secured to the pivot point by a massless spring of spring constant k and unstressed length l. For θ = 0 and at equilibrium m is centered on the rod. Consider motion in a single vertical plane under the influence of gravity. 1. Show that the potential energy is V = k/2(r - L/2)^2 + mgr( 1 - cosθ) – 1/2MgLcosθ. 2. Write the system Lagrangian in terms of r and θ. 3. Obtain the differential equations of motion for r and θ. 4. In the limit of small oscillations find the normal mode frequencies. To what physical motions do these frequencies correspond?