A compact object with a mass of 6.40 kg oscillates at the end of a vertical spring with a spring constant of 2.40 x 10 N/m. The motion is damped by air resistance, and the damping coefficient is b = 3.00 N - s/m. (a) What is the frequency (in Hz) of the damped oscillation? 9.746 Hz (b) By what percentage does the amplitude of the oscillation decrease in each cycle? 2.37 (c) Over what time interval (in s) does the energy of the system drop to 3.00% of its initial value? 0.02 How does the energy depend on amplitude? How does the amplitude depend on the original amplitude and an exponential function? Setting the expression for the current energy equal to the fraction of the original, can you solve this exponential equation for the time? s (d) What If? The atmosphere of Venus is 50 times thicker than that on Earth. If the effect of air resistance on Venus is represented by b = 150 N - s/m, recalculate the answers for parts (a) to (c) for this system if it is set in motion in the atmosphere of Venus. What is the frequency (in Hz) of the damped oscillations? Hz What is the percentage decrease in amplitude in each cycle? % What is the time interval (in s) for the energy to drop to 3.00% of its initial value?

A 10.0 kg object oscillates at the end of a vertical spring that has a spring constant of 1.90 x 104 N/m. The effect of air resistance is represented by the damping coefficient b = 3.00 N-s/m. (a) Calculate the frequency of the dampened oscillation. Hz (b) By what percentage does the amplitude of the oscillation decrease in each cycle? % (c) Find the time interval that elapses while the energy of the system drops to 3.50% of its initial value.

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

A steel ball attached to a spring moves in simple harmonic motion. The amplitude of the ball's motion is 10.5 cm, and the spring constant is 5.00 N/m. When the ball is halfway between its equilibrium position and its maximum displacement from equilibrium, its speed is 18.6 cm/s. (a) What is the mass of the ball (in kg)? kg (b) What is the period of oscillation (in s)? (c) What is the maximum acceleration of the ball? (Enter the magnitude in m/s².) m/s²

A 2-kg mass is attached to a spring hanging from the ceiling, thereby causing the spring to stretch 1.4 m upon coming to rest at equilibrium. At time t= 0, an external force of F(t) = cos 2t N is applied to the system. The damping constant for the system is 4 N-sec/m. Determine the steady-state solution for the system. The steady-state solution is y(t)=- plz help

need help with d

A 2-kg mass is attached to a spring with stiffness 56 N/m. The damping constant for the system is 8√√7 N-sec/m. If the mass is pulled 10 cm to the right of equilibrium and given an initial rightward velocity of 4 m/sec, what is the maximum displacement from equilibrium that it will attain?

The springs of a 1600-kg car compress 4.70 mm when its 66.0-kg driver gets into the driver's seat. If the car goes over a bump, what will be the frequency of oscillations? Ignore damping. Express your answer using three significant figures. ΜΕ ΑΣΦ f= ? Hz

A 3-kg mass is attached to a spring with stiffness 60 N/m. The damping constant for the system is 12√5 N-sec/m. If the mass is pulled 20 cm to the right of equilibrium and given an initial rightward velocity of 4 m/sec, what is the maximum displacement from equilibrium that it will attain?

A spring withk = 35.5 N/m has a mass of 5.50 kg attached to it. An external force F = (4.65 N)sin[(6.80 s¯)t] drives the spring mass system so that it oscillates without any resistive forces. What is the amplitude of the S oscillatory motion of the spring-mass system?