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Problem 13. A block oscillating on a spring is subject to a damping force that is...
6. A spring-mass system is oscillating under no external force, with a damping constant equal to...
6. A spring-mass system is oscillating under no external force, with a damping constant equal to 2 and spring constant equal to 1. If at t = 0 we release (x'(0) = 0) the mass from a stretched position at a displacement of x(0) = 3. Write down the modelling ODE and solve it to find the solution. What will happen eventually to the system? Is it overdamped or undedamped? Will it oscillate?
A car and its suspension system act as a block of mass m= on a vertical spring with k 1.2 x 10 N m, which is damped...
A car and its suspension system act as a block of mass m= on a vertical spring with k 1.2 x 10 N m, which is damped when moving in the vertical direction by a damping force Famp =-rý, where y is the 1200 kg sitting 4. (a) damping constant. If y is 90% of the critical value; what is the period of vertical oscillation of the car? () by what factor does the oscillation amplitude decrease within one period?...
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in...
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in Fig. II-2. The block is moved to the right of the equilibrium position and is released from rest (time t = 0) when its displacement, x = XO. Using the notations given in Fig. II-2,4 (1) Draw the free body diagram of the block - (2) Write the equation of motion of the block- If the initial displacement of the block to the right...
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in...
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in Fig. II-2. The block is moved to the right of the equilibrium position and is released from rest (time t = 0) when its displacement, x = XO. Using the notations given in Fig. II-2,4 (1) Draw the free body diagram of the block - (2) Write the equation of motion of the block- If the initial displacement of the block to the right...
5) A damped simple harmonic oscillator consists of a.40 kg mass oscillating vertically on a spring...
5) A damped simple harmonic oscillator consists of a.40 kg mass oscillating vertically on a spring with k- 15 N/m with a damping coefficient of .20 kg/s. The spring is initially stretched 17 cm downwards and the mass is released from rest. a) What is the angular frequency of the mass? b) What is the position of the mass at t-3 seconds? c) Sketch a position vs time graph for the mass, showing at least 5 full cycles of oscillation....
The force of constant of a spring of spring pendulum is 50N/m. A block of mass...
The force of constant of a spring of spring pendulum is 50N/m. A block of mass 0.5 kg, attached to it is pulled through a distance of 0.01 m before being released. Calculate the following expressions: a) the time period and frequency b) velocity amplitude and acceleration amplitude; c) the time required by the block to move half-way towards the center from its initial position d) total energy of the system.
The term oscillator describes any system that has cyclic or near-cyclic behavior. The periodic motion of...
The term oscillator describes any system that has cyclic or near-cyclic behavior. The periodic motion of a planet or a pendulum, the alternating current in an electrical circuit, the vibrations of cesium atoms in an atomic clock are examples of oscillators. It turns out that many oscillators are governed by differential equations- equations that involve a function and its derivatives. In this project we explore solutions of a common oscillator equation. Imagine a block hanging vertically from a spring that...
2. An 8 lb object stretches a spring 1/2 ft by itself when there is no damper attached. Then, a damper is attached to it that will exert a force of 12 lbs when the velocity is 2 ft/s. Is this...
2. An 8 lb object stretches a spring 1/2 ft by itself when there is no damper attached. Then, a damper is attached to it that will exert a force of 12 lbs when the velocity is 2 ft/s. Is this system over- damped, under-damped, or critically damped? (6 points) a) b) Find the displacement at any time t, u(t). (6 points) c) Sketch of the displacement of the mass for the first 10 seconds. (4 points) d) Discuss the...
A 2.0 kg block on a horizontal frictionless surface is attached to a spring whose force...
A 2.0 kg block on a horizontal frictionless surface is attached to a spring whose force constant is 300 N/m. The block is pulled from its equilibrium position at x = 0 m to a displacement x = + 0.090 m and released from rest t=0 The block then executes SHM along the x-axis horizontal. (a) What is the maximum acceleration and velocity?
A block of mass m is 650 g which is tied to a spring whose spring...
A block of mass m is 650 g which is tied to a spring whose spring constant is 62 N/m. The block is pulled a distance x=11 cm from its equilibrium position at x=0 on a frictionless surface and released from rest at t=0 s. What are the angular frequency, the frequency, and the period of the resulting motion? What is the amplitude of the oscillation? What is the maximum speed Vm of the oscillating block, and where is the...
6. A spring-mass system is oscillating under no external force, with a damping constant equal to 2 and spring constant equal to 1. If at t = 0 we release (x'(0) = 0) the mass from a stretched position at a displacement of x(0) = 3. Write down the modelling ODE and solve it to find the solution. What will happen eventually to the system? Is it overdamped or undedamped? Will it oscillate?
A car and its suspension system act as a block of mass m= on a vertical spring with k 1.2 x 10 N m, which is damped when moving in the vertical direction by a damping force Famp =-rý, where y is the 1200 kg sitting 4. (a) damping constant. If y is 90% of the critical value; what is the period of vertical oscillation of the car? () by what factor does the oscillation amplitude decrease within one period?...
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in Fig. II-2. The block is moved to the right of the equilibrium position and is released from rest (time t = 0) when its displacement, x = XO. Using the notations given in Fig. II-2,4 (1) Draw the free body diagram of the block - (2) Write the equation of motion of the block- If the initial displacement of the block to the right...
A spring-mass-dashpot system for the motion of a block of mass m kg is shown in Fig. II-2. The block is moved to the right of the equilibrium position and is released from rest (time t = 0) when its displacement, x = XO. Using the notations given in Fig. II-2,4 (1) Draw the free body diagram of the block - (2) Write the equation of motion of the block- If the initial displacement of the block to the right...
5) A damped simple harmonic oscillator consists of a.40 kg mass oscillating vertically on a spring with k- 15 N/m with a damping coefficient of .20 kg/s. The spring is initially stretched 17 cm downwards and the mass is released from rest. a) What is the angular frequency of the mass? b) What is the position of the mass at t-3 seconds? c) Sketch a position vs time graph for the mass, showing at least 5 full cycles of oscillation....
The term oscillator describes any system that has cyclic or near-cyclic behavior. The periodic motion of a planet or a pendulum, the alternating current in an electrical circuit, the vibrations of cesium atoms in an atomic clock are examples of oscillators. It turns out that many oscillators are governed by differential equations- equations that involve a function and its derivatives. In this project we explore solutions of a common oscillator equation. Imagine a block hanging vertically from a spring that...
2. An 8 lb object stretches a spring 1/2 ft by itself when there is no damper attached. Then, a damper is attached to it that will exert a force of 12 lbs when the velocity is 2 ft/s. Is this system over- damped, under-damped, or critically damped? (6 points) a) b) Find the displacement at any time t, u(t). (6 points) c) Sketch of the displacement of the mass for the first 10 seconds. (4 points) d) Discuss the...
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PLEASE DON'T ANSWER IF YOU CAN'T ANSWER ALL OF THE QUESTIONS. I
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Consider...
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