A spring with constant k = 5 N/m hanging from the ceiling is placed at its lower end with an object of 1 N, which causes it to remain in equilibrium. The weight is then pulled 0.5 m above the equilibrium position. and is released with no initial velocity. There is no damping force acting on the system. SI x(t) represents the displacement of the weight, in meters, from the equilibrium point and taking upwards as the positive direction, an equation that describes the position of the weight as a function of time t (in seconds) is: If necessary, use the gravity

An object weighing 32 lb stretches a spring 2ft in equilibrium. There is also a damping force with c = 8. The spring is raised 2 ft and thrown upwards with a velocity of 4ft/sec. Determine the mass m and the spring constant k, and give the differential equation describing the harmonic motion of this system. Solve the differential equation to find the displacement y.

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 metal sphere with a mass of 4.00 kg oscillates at the end of a vertical spring with a spring constant of 2.20 x 104 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? 11.802 Hz (b) By what percentage does the amplitude of the oscillation decrease in each cycle? 3.1 % (c) Over what time interval (in s) does the energy of the system drop to 3.00% of its initial value? 4.68 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 150 N · s/m, recalculate the answers for parts (a) to (c) for this system if it is set in motion in the represented by b atmosphere of Venus. What is the frequency (in Hz) of the damped oscillations? 11.419 Hz What is the percentage decrease in amplitude in each cycle? 74.45 Follow the same steps as in part (b), only use the new value of b. Remember the angular frequency has now changed as…

The suspension system of a 2100 kg automobile "sags" 7.0 cm when the chassis is placed on it. Also, the oscillation amplitude decreases by 45% each cycle. Estimate the values of (a) the spring constant k and (b) the damping constant b for the spring and shock absorber system of one wheel, assuming each wheel supports 525 kg. (a) Number (b) Number 73500 Units N/m Units kg/s 4

A spring with spring constant k=12.5N/m is hung vertically. A mass of 0.500 kg is then suspended from the spring. Determine the displacement of the spring’s end due to the weight of the 0.500 kg object.

An oscillating block-spring system takes 0.635 s to begin repeating its motion. Find (a) the period, (b) the frequency in hertz, and (c) the angular frequency in radians per second.

A block of mass m = 600 g is attached to a horizontal spring with a spring constant of k = 3.6 N m¹. When it is in motion, the system is damped by a force Fdamp = -4.2x (SI units). At time t = 0, the block is pulled out to a position x(0) = -20 cm relative to its equilibrium, and set in motion with a velocity (0) = -1.3 m s¯¹. Find the displacement and the velocity of the block as functions of time thereafter.

A body with mass of 250 g is attached to the end of a spring that is stretched 25 cm by a force of 9 N. At time t=0 the body is pulled 1 m to the left. stretching the spring, and set in motion with an initial velocity of 5 m/s to the right. (a) Find x(t) in the form C cos (-a). (b) Find the amplitude and the period of motion of the body.

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