A mass weighting 24 lbs stretches a spring 4 inches. The mass is in a medium that exerts a damping force of 57 lbs when the mass has a speed of 6 ft/sec. Suppose the object is displaced an additional 8 inches and released. Find an equation for the object's displacement, u(t), in feet after t seconds. u(t) = Use the convention: If the displacement is upward then u < 0
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- A mass m = 2.75 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 = 0.25 Hz Part (a) Write an equation for the spring constant k. Part (b) Calculate the spring constant k, in Newtons per meter. Part (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. Part (d) Calculate the total mechanical energy E, in joules. Part (e) If the amplitude is doubled, what happens to the total mechanical energy? Choose the best answer: E is halved. E remains unchanged. It cannot be determined with the information provided. E increases by a factor of four. E doubles.A spring is suspended from a support and a meter stick is placed next to the spring. Different masses are hung from the bottom of the spring and the length of the spring stretch is recorded. Which is the independent (manipulated) variable in this investigation? O the kind of spring O the type of support O the amount of mass O the type of meter stick ell 5 g 10 g 20 gAfter landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 50.0 cm. She finds that the pendulum makes 100 complete swings in 136 s. What is the value of g on this planet? (10.7 m/s³)
- A 2.2-kg object is suspended from a spring with k = 66 N/m. The mass is pulled 0.88 m downward from its equilibrium position and allowed to oscillate. What is the maximum kinetic energy of the object? ROUND OFF ANSWER UP TO 2 DECIMAL PLACES. INPUT BOTH THE NUMBER AND THE UNIT (ABBREVIATION OF UNIT ONLY).In a spring-mass experiment, a hanging spring is stretched by 5 cm when a mass of 156 g object is attached to it. When the mass is put to oscillate, the sensor measured a maximum speed of 3.84 m/s. Take g = 9.8 m/s². b) What is the spring constant value? At what position(s) will the object have a speed 1/2 that of the maximum speed? Take y = 0 at the equilibrium and upward is a positive direction. At t = 0, the object is moving at 1/2V max away from the equilibrium with the spring compressed. Using y (t) = A cos(wt + 0), write a complete expression with numerical values and units to describe the motion of the object.Please help.
- Imagine you've constructed a pendulum at home and measured the length of the rope and the period. The goal here is to create a graph where the slope corresponds to the gravitational acceleration constant. For that you have to get an X and a Y. First, you have these 2 equations as a starting point: T= 2π/ω and ω= sqrt(g/L). Play with the equations to construct an equation for a linear graph with the form: Y=mX+b where the slope m=g. Identify clearly what X and Y represent. The equation should look like: ? = g(? + ?)A force of 540 newtons stretches a spring 3 meters. A mass of 45 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 10 m/s. Give the initial conditions. x(0) = x'(0) = m m/s Find the equation of motion. x(t) = mWrite down the expression for period of a pendulum of length I and the gravitational field strength g. Please use Il * II for products (e.g. B*A), "/" for ratios (e.g. B/A) and the usual "+" and "-" signs as appropriate. For square root and power please use sqrt(A*B) and (A*B)^2. Please use the "Display response" button to check you entered the answer you expect. T=
- A small insect of mass 0.25 g is caught in a spider's web. The web oscillates predominantly with a frequency of 2.70 Hz. What is the value of the effective spring stiffness constant k (in N/m) for the web? Type your answer correct to within two decimal places. Use a period (full stop) for a decimal place, eg. 500.00 - Do not use a comma or input your answer in some form of scientific notation. Do NOT include units in your answer. Type your answer.A mass on a spring oscillates 43.0 times in 13.2 s. What is the frequency of the oscillation? For the oscillator in Problem 5, how many oscillations would it make in 2.0 s?Q1. Consider a spring mass system given in Fig 1 with mass of 1kg attached to a spring with K=10. The motion is damped with C=6 and is being driven by a force given by 25 cos 4t . If the spring is released from rest, find the equation of displacement y(t). Note: You cannot use the direct formulas for constants in particular solution. Spring Mass r(t) Dashpot Fig. 1