For a damped spring and block oscillator, the mass of the block is 0.2 kg, the spring constant is 90 N/m and the damping constant is 0.06 kg/s. Calculate (i) the period of oscillation (ii) the time taken for its amplitude co become half its initial value.
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- For the damped oscillator system , the block has a mass of 1.50 kg and the spring constant is8.00 N/m.The damping force is given by =b(dx/dt), where b 230g/s. The block is pulled down 12.0 cm and released. (a) Calculatethe time required for the amplitude of the resulting oscillations tofall to one-third of its initial value. (b) How many oscillations aremade by the block in this time?A 0.110 kg body undergoes simple harmonic motion of amplitude 7.19 cm and period 0.500 s. (a) What is the magnitude of the maximum force acting on it? (b) If the oscillations are produced by a spring, what is the spring constant?A mass of 310 g is suspended from a weightless, inextensible string of length toform a simple pendulum. The mass is now pulled aside so that the string makesan angle of 7.5 with the vertical and then released.The frequency of the resulting oscillation is measured and found to be 0.512 Hz calculate the maximum tension in the string answer: 3.21N
- A 350 g mass on a 45cm long string is released at an angle of 4.5° from vertical. It has a damping constant of 0.010 kg/s. After 25s (a) how many oscillations has it completed and (b) how muchenergy has been lost?An old car with worn-out shock absorbers oscillates with a particular frequency when ithits a speed bump. What would happen to the oscillation frequency if the car had anadditional passenger?(A) it would increase(B) it would decrease(C) it would remain unchanged(D) no oscillations would occurA boy of mass 49.8 kg standing on the end of a diving board depresses it vertically downward a distance of 15.7 cm. By pushing down on the board with a force a little greater than his weight, the boy can depress the end of the board a bit farther. The boy and the board then oscillate up and down. Estimate the period of oscillation, assuming that the force the board exerts is approximately like that of a compressed spring, in other words, that it obeys Hooke's law.
- A system with 100g_mass and a spring constant of k=150N/m has a damping constant y=1.1. ASsume the mass was pulled to the right 30 cm at t=0and released. a)Estimate the time at which the amplitude has decayed to ¼ of its initial value. b)Assume the system is connected to a forcing function given by(in Newtons)F(t)=3coswtEstimate the value of the amplitude at resonance.According to Eq. (21), the amplitude of forced steady periodic oscillations for the system mx" + cx' + kx = Fo cos ot is given by Fo C(@) = V(k – mo²)2 + (co)² (a) If c 2 Cer/2, where cer = V4km, show that C steadily decreases as w increases. (b) If c < cer//2, show that C attains a maximum value (practical reso- nance) when c2 < wo = 2m2 w = Wm =Please help me
- An oscillator consists of a block attached to a spring (k = 405 N/m). At some time t, the position (measured from the system's equilibrium location), velocity, and acceleration of the block are x = 0.0882 m, v = -15.4 m/s, and a = -120 m/s2. Calculate (a) the frequency of oscillation, (b) the mass of the block, and (c) the amplitude of the motion.A block is attached to a spring with a sping constant of 7.6 N/m and it undergoes simple harmonic motion. The amplitude of the blocks motion is 6.30 cm. When the block is halfway between its equilibrium position and the end point of it's motion, its speed is measured to be 28.9 cm/s. Calculate : (a) the mass of the block, (b) the period of the motion, and (c) the maximum acceleration of the block.If the shock absorbers in a car go bad, then the car will oscillate at the least provocation, such as when going over bumps in the road and after stopping. Calculate the frequency and period of these oscillations for such a car if the car’s mass (including its load) is 900 kg and the force constant (k) of the suspension system is 6.53X104 N/m.