Question 4: A mass of 0.2kg attached to a spring is making an underdamping harmonic motion. If the friction coefficient (b) is 2kg/s what is the time required for the amplitude to drop to half of its initial value?
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- In the figure, two blocks (m = 2.30 kg and M = 9.00 kg) and a spring (k = 180 N/m) are arranged on a horizontal frictionless surface. The coefficient of static friction between the two blocks is 0.300. What amplitude of simple harmonic motion of the spring-blocks system puts the smaller block on the verge of slipping over the larger block?You have made a physical pendulum by swinging a rod of mass M = 1.08 kg and length L = 1.45 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 = 19.34 degrees. Solid Rod Swings in Simple Harmonic Motion ^ 0=-0, max 0=+0₁ max Determine all the following: 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, max = radians The angular velocity when 0 = 64% of full swing, w(0 = 0.64 0max): NOTE: The first question requires a FORMULA, not a value. rad/sec = meters rad/secA 3kg block is attached to one end of a spring and resting on a frictionless surface. The mass is pulled away from rest and put to motion. A motion sensor is stationed to capture the data from the motion and we are given the following equation for the speed of the object in meters per second: v=-6.5 sin(4.0t). What would be the amplitude of the motion, the angular frequency, and the spring constant?
- In the figure, two blocks (m = 2.40 kg and M = 12.0 kg) and a spring (k = 260 N/m) are arranged on a horizontal frictionless surface. The coefficient of static friction between the two blocks is 0.350. What amplitude of simple harmonic motion of the spring-blocks system puts the smaller block on the verge of slipping over the larger block? 00000000 m MA 260 g load attached to a horizontal spring moves in simple harmonic motion with a period of 0.450 s. The total mechanical energy of the spring–load system is 2.00 J. What is the spring constant (in N/m)? What is the amplitude (in m) of the motion? What If? What is the percentage change in amplitude of motion if the total energy of the system is increased to 6.00 J (% change)?A block-spring system consists of a spring with constant k = 405 N/m attached to a 1.00 kg block on a frictionless surface. The block is pulled 6.10 cm from equilibrium and released from rest. For the resulting oscillation, find the amplitude, angular frequency, frequency, and period. What is the maximum value of the block's velocity and acceleration? (a)amplitude (in m) m (b)angular frequency (in rad/s) rad/s (c)frequency (in Hz) Hz (d)period (in s) s (e)maximum velocity (in m/s) m/s (f)maximum acceleration (in m/s2) m/s2
- A 500 g mass is hung from a vertical spring and allowed to come to rest or its equilibrium position. As a result, the spring is stretched by 10 cm. The mass is then pulled down an additional 15 cm and released so that it oscillates in a SHM. Find the amplitude and frequency of the SHM and write down the equation of the position as a function of time.An 9-kg mass is attached to a spring hanging from the ceiling and allowed to come to rest. Assume that the spring constant is 20 N/m and the damping constant is 4 N-sec/m. At time t= 0, an external force of 8 sin 2t cos 2t is applied to the system. Determine the amplitude and frequency of the steady-state solution. The amplitude is (Type an integer or a decimal. Round to four decimal places as needed.)A harmonic oscillator has angular frequency w and amplitude A. Assume that the elastic potential energy of the oscillator is zero at x = 0. At an instant when the displacement is equal to A/5, what fraction of the total energy of the oscillator is kinetic? Give the final answer to 2 decimal places.