11. A vertical spring of spring constant 115 N/m supports a mass of 75 g. The mass oscillates in a tube of liquid. If the mass is initially given an amplitude of 5.0 cm, the mass is observed to have an amplitude of 2.0 cm after 3.5 s. Estimate the damping constant b. Neglect buoyant forces.
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- 2. The amplitude of a damped oscillator decays to half of its initial value in 22 seconds. How much additional time is required for the amplitude to decay to one quarter of its initial value?3. A 200g air glider is set up to move with almost no friction on a track. It has springs attached to both ends which give the system a combined spring constant of 30 N/m. At time t = 0, the glider has a velocity of 1.5 m/s 2 and is located at the equilibrium position. For this system, find the amplitude, period, angular frequency, and total energy, and write an equation of motion for the system.1. A pendulum with mass 2kg, length 2.5m swings with amplitude A = 2cm. After a long time the amplitude decreases to 1 cm due to air drag. How long is the period after the amplitude decrease? 2. What is the period of oscillation of the pendulum before and after the amplitude change?
- 1. If a spring has a spring constant of 23.0 N/m² then how much force is required to stretch it 11.0 cm from equilibrium? s Y91909 of a simple harmonic oscillator ever zero? If so, where?4. An object of mass of 3.20 kg oscillates in a spring whose constant k = 300 N/m. Its oscillation frequency is 1.67 Hz. (a) Determine the angular frequency of the damped oscillations and the value of the damping constant b for that angular frequency. (b) What value of b would give us a critically damped motion?For the graph as shown, determine the frequency f and the oscillation amplitude A.
- 3. A 20 g block is attached to a spring and oscillates at 2.0 Hz. At one instant, the block is at x = 5.0 cm and has a velocity v = -30 cm/s Find the amplitude and the period of the motion.10. A block hangs on a spring attached to the ceiling and is pulled down 6 inches below itsequilibrium position. After release, the block makes one complete up-and-down cycle in 2seconds and follows simple harmonic motion. a. What is the period of the motion? b. What is the frequency? c. What is the amplitude? d. Write a function to model the displacement ? (in inches) as a function of the time ? (in seconds) after release. Assume that a displacement above the equilibrium point is positive.e. Find the displacement of the block and direction of movement at ? = 1 sec.3. The MacKay Bridge over Halifax Harbour is designed to sway in high wind conditions to help absorb shock. If you were to measure the sway of the bridge in an 80 km/hr wind, you would find the following results: At t = Os, the sway = +45 cm (45 cm right) At t = 14s, the sway = -45 cm (45 cm left) a) What is the period of the swaying bridge? The amplitude? b) What is the equation of the sinusoidal axis? c) Construct a table of values and graph demonstrating one full cycle of motion. d) Suppose dampers were added to reduce the sway (but not period) by 50%. Construct a new table of values and graph to demonstrate one full cycle.
- 64) A 7 gr bullet is fired into a 750 gr block of wood which is at rest on a frictionless table (Isolated System) and attached to a spring with a spring constant of 8000 N/m. The bullet has a velocity of 720 m/sec and is trapped inside the block of wood. a) What is the velocity of the block before the collision? b) What is the velocity of the block/bullet after the collision? c) What is the Amplitude of the resulting SHM? d) What is the kinetic energy after the collision? e) What is the potential energy after the collision? f) What is the mechanical energy after the collision? g) What is the kinetic energy at maximum compression of the spring? h) What is the potential energy at maximum compression of the spring? i) What is the mechanical energy at maximum compression of the spring? (2A 75 kg mass is attached to an ideal massless spring with a spring constant of 15 N/m oscillates on a horizontal, frictionless track. A time t=0.00 s, the mass is released from rest at x=10 cm. a- Find the frequency of the oscillations. b-determin the maximum speed of the mass. At what point in the motion does the maximum speed occur? c-What is the maximum acceleration of the mass? At what point does the maximum acceleration occur? d-Determin the total energy of the oscillating system. e-Express the displacement x as a function of time