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A spring-mass system with m = 50kg and k = 4000N/m shown in Figure Q3(a). If the mass is released from its equivalent position and results in
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(i) Starting from a free body diagram, derive the equation of motion.
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- A block of mass m = 3kg is attached to a light spring with a spring constant k and moves in simple harmonic motion on a frictionless horizontal surface. Initially the spring is compressed to x, = -–0.1 m from its equilibrium position and is given an initial velocity vo in the negative x-direction, as shown in the figure below. The maximum speed reached by the block is vmax = v2 m/s. The block's period of oscil- lation is T= 0.889s. 3) The velocity of the block att = 0, vo is: hmmo Equilibnura aV2 m/s b. V2 m/s e. -1 224 m/s d 1224 m/s wwwQUESTION 4 Q 4(a) The force, F, required to compress a spring is given by F = 1000x + 50x³, where x is displacement from its unstretched length. The work done, W, to compress a spring by 0.3m is given by 0³ F dx. Determine W, giving your answer correct to 2 significant figures. Q 4(b) The velocity, v, of a piston moving with simple harmonic motion at time, t, is given by v = 20sin (3t) Find in terms of TT, the mean velocity between t = 0 and t = =F Q 4(c) Sketch the region bounded by the curve f(x) = and the line g(x) = 3 - x, for 0 ≤ x ≤ 3. Use integration, determine the area enclosed by the curves, giving your answer correct to 4 decimal places.Calculate the velocity of a simple harmonic oscillator with amplitude of 13.5 cm and frequency of 5 Hz at a point located 5 cm away from the equilibrium position. Give your answer in Sl units.
- Calculate the velocity of a simple harmonic oscillator with amplitude of 24 cm and frequency of 5 Hz at a point located 5 cm away from the equilibrium position. Give your answer in Sl units. Answer: Choose... Previous page Next pageA mathematical pendulum swings with angular amplitude α (α ≪ 1), its period is T . By what factor does the period of the pendulum change if it is suddenly surrounded by two perfectly elastic walls (see figure)? The walls are arranged symmetrically, their angular distance is α.A stiff spring k = 666 N/m has be attached to the floor vertically. A mass of 6.66 kg is placed on top of the spring as shown below and it finds a new equilibrium point. If the block is pressed downward and released it oscillates. If the compression is too big, however, the block will lose contact with the spring at the maximum vertical extension. Draw a free body diagram and find that extension at which the block loses contact with the spring.
- A car with a mass m = 1000.0kg is moving on a horizontal surface with a speed v = 20.0m/s when it strikes a horizontal coiled spring and is brought to rest when the spring is compressed by a distance d = 3.0m. Calculate the spring stiffness constant k by... (a) select appropriate common equations and make appropriate substitutions that are specific to the problem, and algebraically manipulate the equations to end with an algebraic expression for the variable the problem is asking you to solve for. (b) Show the numeric substitution of given quantities and show the final numeric result. (c) Draw a free body diagram for the system and define the given quantities.A mass-spring-dashpot system is modeled by the differential equation: x" + 4x + 5x = f(t) (a) What is the type of oscillatory motion of the mass? Explain. (b) Find the transient solution of the system. (c) Find the steady state solution of the system for f(t) = 4 cos wt for w= 1. Write your solution as C cos (wt -a). (d) Solve the initial value problem for z(0) = 12, x'(0) = 0. (e) Draw the steady state solution and describe the oscillation.A mass weighing 8 pounds is attached to a spring. When set in motion, the spring/mass system exhibits simple harmonic motion. (a) Determine the equation of motion if the spring con- stant is 1 lb/ft and the mass is initially released from a point 6 inches below the equilibrium position with a downward velocity of ft/s.
- Asap plzCalculate the velocity of a simple harmonic oscillator with amplitude of 11.4 cm and frequency of 5 Hz at a point located 5 cm away from the equilibrium position. Give your answer in Sl units. Answer: Choose...The potential energy of an object attached to a spring is 2.40 J at a location where the kinetic energy is 1.70 J. If the amplitude A of the simple harmonic motion is 20.0 cm, calculate the spring constant k and the magnitude of the largest force Fspring, max that the object experiences.