A disk of radius 0.25 m is attached at its edge to a light (massless) wire of length 0.50 m to form a physical pendulum.  Assuming small amplitude motion, calculate its period of oscillation.  For a disk, I = (1/2)MR2 about its center of mass.

A uniform stick of length L and mass m is pivoted at one of its ends. Derive an equation for the period of oscillation when the stick is set into small oscillation. Answer in terms of m, g, and L as needed.

(B) llllllll Students set up an experiment by attaching an ideal vertical spring to a support and hanging a block of known mass from the spring. The students pull the block down and release it from rest. The students then measure the period of the block's oscillation. This procedure is repeated for several trials using the same spring but with blocks of different known masses. The students are instructed to create a linear graph using the mass m of each block and the period T of the block's motion. The slope of the graph will be used to calculate the force constant k of the spring. Which of the following best indicates how the students should create their linear graph and how k can be calculated from the slope of the graph? E k Graph T on the vertical axis and m on the horizontal axis; set k = 2π slope Graph T² on the vertical axis and m on the horizontal axis; set k Graph T on the vertical axis and m² on the horizontal axis; set k Graph T² on the vertical axis and m on the horizontal…

A disk of radius 0.25 meters is attached at its edge to a light (massless) wire of length 0.50 meters to form a physical pendulum.  Assuming small amplitude motion, calculate its period of oscillation.             For a disk, I = (1/2)MR2 about its center of mass.

A cart of mass 206 g is placed on a frictionless horizontal air track. A spring having a spring constant of 10.80 N/ m is attached between the cart and the left end of the track. When in equilibrium, the cart is located 10.0 cm from the left end of the track. If the cart is displaced 5.10 cm from its equilibrium position, find(a) the period at which it oscillates   A cart of mass 206 g is placed on a frictionless horizontal air track. A spring having a spring constant of 10.80 N/ m is attached between the cart and the left end of the track. When in equilibrium, the cart is located 10.0 cm from the left end of the track. If the cart is displaced 5.10 cm from its equilibrium position, find (d) its speed when it is 12.0 cm from the left end of the track.

A small steel ball is hanging by a light thread from the ceiling. The steel ball is then displaced 5.0 cm and makes 32 oscillations in exactly 50 s. Determine the period, T, angular frequency, w, and then write the motion of the steel ball as a function of time, t.

A mass-spring-dashpot system is modeled by the differential equation: x" + 4x + 5x = f(t) (a) What is the type of oscillatory motion of the mass? Explain. (b) Find the transient solution of the system. (c) Find the steady state solution of the system for f(t) = 4 cos wt for w= 1. Write your solution as C cos (wt -a). (d) Solve the initial value problem for z(0) = 12, x'(0) = 0. (e) Draw the steady state solution and describe the oscillation.

A mass 3,476g is attached to an ideal spring. Once set in motion the mass-spring system is a harmonic oscillator. This mass spring system has a total mechanical energy of 0.503.J. If the oscillation amplitude is 8.723cm, what is the period of oscillation (in s)?

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In order to study the long-term effects of weightlessness, astronauts in space must be weighed (or at least "massed). One way in which this is done is to seat them in a chair of known mass attached to a spring of known force constant and measure the period of the oscillations of this system. The 36.4-kg chair alone oscillates with a period of 1.25 s, and the period with the astronaut sitting in the chair is 2.24 s. Part A Find the force constant of the spring Express your answer in newtons per meter. k= N/m Submit Request Answer • Part B Find the mass of the astronaut. Express your answer in kilograms. kg