Chapter 15, Problem 058 For a damped oscillator with a mass of 240 g, a spring constant 130 N/m and a damping coefficient of 62 g/s, what is the ratio of the amplitude of the damped oscillations to the initial amplitude at the end of 21 cycles? Number Units the tolerance is +/-1 in the 2nd significant digit
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- A mass m = 3.3 kg is at the end of a horizontal spring on a frictionless horizontal surface. The mass is oscillating with an amplitude A = 4.5 cm and a frequency f = 1.5 Hz. a. Write an equation for the spring constant k. b. Calculate the spring constant k, in Newtons per meter. c. Write an equation for the total mechanical energy, E, of the motion. Your expression should be in terms of the variables in the original problem statement. d. Calculate the total mechanical energy E, in joules.Consider a critically damped oscillator with w=y and mass m that is driven by force Fa cos(wat). ▼ Part A - What is the amplitude of the steady-state oscillation at wa=0? Answer symbolically. You can type y as \gamma. You can type Fa as F_d Ao = Submit IVE ΑΣΦ Fd k Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining Wd = Part B - The maximum amplitude of oscillation, Ao, occurs for wa = 0. At what driving frequency does the amplitude equal to Ao/2? Answer symbolically. You can type y as \gamma. You can type Fa as F_d Submit ? IVE ΑΣΦ Request Answer ?Chapter 15, Problem 24 Z Your answer is partially correct. Try again. In the figure, two springs are joined and connected to a block of mass 40.3 kg that is set oscillating over a frictionless floor. The springs each have spring constant k = 242 N/m. What is the frequency (in Hz) of the oscillations? Number Units THz the tolerance is +/-2%
- Grandfather clocks keep time by advancing the hands a set amount per oscillation of the pendulum. Therefore, the pendulum needs to have a very accurate period for the clock to keep time accurately. As a fine adjustment of the pendulum’s period, many grandfather clocks have an adjustment nut on a bolt at the bottom of the pendulum disk. Screwing this nut inward or outward changes the mass distribution of the pendulum by moving the pendulum disk closer to or farther from the axis of rotation at O. Let mp = 0.7 kg and r = 0.1 m Model the pendulum as a uniform disk of radius r and mass mp at the end of a rod of negligible mass and length L – r, and assume that the oscillations of θ are small. If the pendulum disk is initially at a distance L = 0.85 m from the pin at O, how much would the period of the pendulum change if the adjustment nut with a lead of 0.5 mm was rotated four complete rotations closer to the disk? In addition, how much time would the clock gain or lose in a 24 h…Physics A simple pendulum consists of a small object of mass m= 1.52 kg hanging under a massless string of length L= 8 m. The pendulum swings with angular frequency ω=5.77 rads. If the mass is changed to 2 m and the length of the string is change to 6 L, the frequency of this new pendulum becomes nω . What is the value of n? Please round your answer to 2 decimal places.K ( thevine white 51649 1₁ Class Work ADVANCED PLACEMENT PHYSICS 1 EQUATIONS, EFFECTIVE ELECTRICITY MECHANICS acceleration A amplitude C. No - FM E e energy frequency f F = force K kinetic energy spring constam Wal- Langular mothentom (length P = power P momentum U 1.99 T= period wtime V b. Find the acceleration each mass. radius or separation W R-E! A 7. AV potential energy volume P-TAV R-ER What is the tension force in the rope? F 4 15 kg 1 = Jonash - speed work done on a system position scceleration w power charge 12 kg O 1. "A 12 kg load hangs from one end of a rope that passes over a small frictionless pulley. A 15 kg counterweight is suspended from the other end of the rope. The system is released from rest & time V a. Draw a free-body diagram for each object showing all applied forces in relative scale. Next to each diagram show the direction of the acceleration of that object. d. What distance does the 12 kg load move in the first 3 s? TEQUESEN What is the velocity of 15 kg…
- A simple pendulum oscillates with a frequency of 6.1 Hz. How long (in centimeters) is the pendulum?A mass weighing 8 lbs stretches a spring 8 inches. The mass is pushed upwards, contracting the spring a distance of 2 inch and then set in motion with a downward velocity of 4 ft/sec. The mass is attached to a viscous damper that exerts a force of 6 pounds when the velocity of the mass is 3 ft/s. Use g = 32 ft/sec² . a) Determine the mass m, spring coefficient K, and the damping coefficient y. b) Write an initial value problem to model the system and solve your IVP to find the position function u(t), for any time t. c) Determine the quasi-frequency µ , period T4, phase shift 8, and amplitude R of the vibration. Use this information to write your position function u(t), as a single term.An object attached to a spring undergoes simple harmonic motion modeled by the differential equation d²x + kx = 0 where x (t) is the displacement of the mass (relative to equilibrium) at time t, m is the dt² mass of the object, and k is the spring constant. A mass of 6 kilograms stretches the spring 0.6 meters. Use this information to find the spring constant. (Use g = 9.8 meters/second²) m k = The previous mass is detached from the spring and a mass of 8 kilograms is attached. This mass is displaced 0.15 meters above equilibrium and then launched with an initial velocity of 2 meters/second. Write the equation of motion in the form x(t) = c₁ cos(wt) + c₂ sin(wt). Do not leave unknown constants in your equation. x(t) Rewrite the equation of motion in the form ä(t) = A sin(wt + p), where 0 ≤ ☀ < 2π. Do not leave unknown constants in your equation. x(t) =
- The block is at rest as shown. What is the peiod of the oscillation if the block is pulled down by 10 cm, in seconds? Use g = 10 m/s2. Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.Letters A-D if possible