A damped oscillator has mass m=5.3 kg, spring constant k = 27 N/m, and viscous force constant c = 11 Ns/m. A periodic driving force with amplitude 14 N is applied to the oscillator, causing it to undergo oscillatory motion. The motion is initially composed of two components, the driven oscillation and the transient oscillation. How long after the external force is initially applied would the transient motion have essentially died out (say, to less than 5% of its initial value)? O about 1 min O about 1 s O about 30 s O about 10 ms
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- The properties of a spring are such that a load of 10 g produces an extension of 1.4 cm. A mass of 0.1 kg hangs at the end of the spring in equilibrium. The mass is then pulled vertically downward through a distance of 6 cm and released. Calculate the period of vibration of the 0.1 kg mass. Give your answer in SI units.You have made a physical pendulum by swinging a rod of mass M = 0.61 kg and length L = 0.86 meters around its end. The mass of the rod is distributed uniformly along its length. We will assume that the amplitude of the swing is max = 14.67 degrees. Solid Rod Swings in Simple Harmonic Motion Ө=-0max Determine all the following: 0=+0₁ max The FORMULA for the moment of inertia of your rod, I = The distance from the pivot point to the Center-Of-Mass, d = The angular frequency of the pendulum, w = The amplitude of the motion in radians, 8max = The angular velocity when 0 = 65% of full swing, w(0 = 0.65 0max) NOTE: The first question requires a FORMULA, not a value. rad/sec radians = meters rad/secA 0.500-kg mass is suspended from a string, forming a pendulum. The period of this pendulum is 3.65 s when the amplitude is 1.00 cm. The mass of the pendulum is now reduced to 0.250 kg. What is the period of oscillation now, when the amplitude is 2.00 cm?
- A solid iron cube is attached to spring-like device and is able to oscillate horizontally with negligible friction. Each side of the cube is 1.50 cm long. The cube is initially pulled to a point where it stretches the spring-like device by 2.75 cm where it is held at rest with a horizontal force of 1.45 N. What is the frequency at which it oscillates when it is released? (Assume the density of iron is 7.86 g/cm3.)A 0.500-kg mass is suspended from a string, forming a pendulum. The period of this pendulum is 1.58 s when the amplitude is 1.00 cm. The mass of the pendulum is now reduced to 0.250 kg. What is the period of oscillation now, when the amplitude is 2.00 cm?A 0.900 kg block sliding on a horizontal frictionless surface is attached to a horizontal spring with k= 420 N/m. Let x be the displacement of the block from the position at which the spring is unstretched. At t= 0 the block passes through x = 0 with a speed of 4.20 m/s in the positive x direction. What are the (a) frequency and (b) amplitude of the block's motion? (a) Number i Units (b) Number i Units
- A 1.5 kg mass is attached to a vertically oriented spring, stretching it 0.45 m. The mass is moved upwards 0.25 m from its equilibrium position and held. A 0.8 kg mass is added to the hanging mass and the total mass is released from rest. What is the amplitude of motion for the two mass system?A 500-g object connected to a light spring with a spring constant of 10.0 N/m sits on a frictionless horizontal table. Suddenly, the object is hit by a force causing it to move towards left and then vibrate back and forth with an amplitude of 10.0 cm. See attached image. (a) Circle the graph below which best describes the position of the objector as a function of time (b) Circle the position(s) where the object experiences maximum acceleration. (c) Determine the value of this maximum acceleration.A spring oscillator is designed with a mass of 0.288 kg. It operates while immersed in a damping fluid, selected so that the oscillation amplitude decreases to 1.00% of its initial value in 7.55 s. Determine the damping coefficient b of the system. Assume that the system is underdamped. b = kg/s
- You attach one end of a spring with a force constant k = 813 N/m to a wall and the other end to a mass m = 1.42 kg and set the mass-spring system into oscillation on a horizontal frictionless surface as shown in the figure. To put the system into oscillation, you pull the block to a position x - 5.76 cm from equilibrium and release it. k x= 0 x=x/4 X = X (a) Determine the potential energy stored in the spring before the block is released. (b) Determine the speed of the block as it passes through the equilibrium position. m/s (c) Determine the speed of the block when it is at a position X¡/4. m/sMultiple-Concept Example 6 presents a model for solving this problem. As far as vertical oscillations are concerned, a certain automobile can be considered to be mounted on four identical springs, each having a spring constant of 1.28 x 105 N/m. Then, four identical passengers are seated in the car, and it is set into a vertical oscillation that has a period of 0.387 s. If the mass of the empty car is 1560 kg, determine the mass of each passenger. Assume that the mass of the car and its passengers is distributed evenly over the springs.A block of mass (3 kg) lays on a frictionless plane and is attached to a horizontal spring with a spring constant (8 N/m). The spring is attached to a nearby vertical wall. The minimum distance of the block from the wall during its oscillations is 0.8 m. The maximum distance of the block from the wall during its oscillations is 1.2 m. If we start a stopwatch (t = 0) when the block is at its closest point to the vertical wall, how far the block from the wall after a time t = 5/4 T? A=0.2 m V= 0.326 T= 0.383s