When a certain simple pendulum is set swinging, its angular displacement theta as a function of time t obeys the equation theta= 8.5° cos(2.4 t). How long is the pendulum?
When a certain simple pendulum is set swinging, its angular displacement theta as a function of...
The angle that a swinging simple pendulum makes with a vertical obeys the equation where the length of the pendulum is 1.207m. a. what is the vertical distance (in cm) between the pendulum bob's highest and lowest positions? b. what is the pendulums max angular speed and max angular accleration? c. what is the pendulum bob's speed (in m/s) at it's lowest position?
2. The angular displacement e(t) of a damped forced pendulum of length 1 swinging in a vertical plane under the influence of gravity can be modelled with the second order non-homogeneous ODE 0"(t) + 270'(t) +w20(t) = f(t), (2) where wa = g/l. The second term in the equation represents the damping force (e.g. air resistance) for the given constant 7 > 0. The model can be used to approximate the motion of a magnetic pendulum bob being driven by...
A certain simple pendulum consists of a small 750.0 ? bob that swings on the end of a 25.0 ?? string. The small amplitude of the oscillations of this pendulum decays to half its original value after 45.0 oscillations. The angular position of the pendulum as a function of time, ?(?), can be expressed as follows. ?(?) = ??0 ? − ??/2m cos(? ′ ? + ?) ??0 is the original angular amplitude. ? is the time, and ? is...
Problem 1 The length of a simple pendulum is 0.68 m and has an angular amplitude of 129. Write an equation of the angular displacement as function of the time.
#2. [Swinging Disk] A uniform circular disk of mass M and radius R is set swinging side-to-side about a frictionless pivot P at its edge (a) What is the disk's moment of inertia about the pivot? (b) Write an expression for the net torque acting on the disk about the pivot when the disk is displaced to the right by angle θ CM (c) Write Newton's 2nd Law for Rotation for the disk when it is displaced as shown. Be...
When is the displacement in simple harmonic motion maximum? If the length of a simple pendulum with a period T is reduced to half of its original value, what would be its new period (in terms of T)? Which one is more elastic? Rubber or steel? Explain. An 80-cm-long, 1.0-mm-diameter steel guitar string must be tightened to a tension of 2000 N by turning the tuning screws. By how much is the string stretched? Young’s Modulus of elasticity for steel...
A simple pendulum is swinging back and forth through a small angle, its motion repeating every 1.34 s. How much longer should the pendulum be made in order to increase its period by 0.27 s?
A simple pendulum is swinging back and forth through a small angle, its motion repeating every 1.36 s. How much longer should the pendulum be made in order to increase its period by 0.29 s?
1. The angular displacement e(t) of an undamped pendulum of length l swinging in a vertical plane under the influence of gravity can be modelled with the nonlinear second order ODE 0"(t) + "$(0(e) – Pef) = = 0, (1) where w2 = { (a) Re-write equation (1) as a system of first-order ODEs by defining (1 = 0(t) and 02 = 't). (b) Find the nullclines and equilibrium points for the system of first-order ODEs. (c) The first order...
During a certain time interval, the angular position of a swinging door is described by θ = 5.04 + 9.7t + 2.10t2, where θ is in radians and t is in seconds. Determine the angular position, angular speed, and angular acceleration of the door at (a) t = 0 and (b) t = 2.95 second. PLEASE WRITE STEP BY STEP HOW YOU GOT THE ANSWER, I'D LIKE TO UNDERSTAND HOW IT WAS SOLVED! THANK YOU