ind the steady-state solution of the system in Fig. 70 when m = 4, c = 4, k = 17 and the driving force is 202 cos 3t. Find the solution corresponding to initial displacement 10 and initial velocity 0.
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Find the steady-state solution of the system in Fig. 70 when m = 4, c = 4, k = 17 and the driving force is
202 cos 3t. Find the solution corresponding to initial displacement 10 and initial velocity 0.
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- Answer within 5 minutesA block of mass, m = 0.5 kg is used to compress a spring with a spring con- 78.4 N/m a distance x from it's resting point. The block is then stant, k released and travels towards a circular loop of radius, R = 1.5 m. The loop and the surface as frictionless except for the region, of length 2.5 m, defined by AB which has a coefficient of friction, µk = 0.3. Determine the minimum compression of the spring that allows for the block to just make it through the loop-to-loop at point C (Hint: This problem is best done by starting at the end and working backwards). R k A Вphy
- A block of mass m is at the top of an inclined plane of length L and angle 0. At the bottom of the plane there is a relaxed spring with spring constant k. (See the figure.) The block is released from rest and slides without friction down the plane. At the bottom of the plane, the block strikes the spring and momentarily comes to rest by compressing the spring by some amount D. (a) Find D in terms of m, k, L, g, and 0. (b) Describe in words what the motion will look like over time.9a.) A particle with mass m is dropped with zero initial velocity a height h above the ground, under the action of the gravitational field (acceration constant g), such that it reaches the ground (z=0) with zero potential energy and velocity v>0. Determine h, in terms of the other quantities given. b.) Another particle moves with Simple Harmonic Motion with centre O.The particle has velocity 13ms–1 when it is 3m from O and 5ms–1 when it is 5m from O.(i) Find the period and amplitude of the motion
- A 5-kg sphere is dropped from a height of y= 3 m to test a new spring floor used in gymnastics. The mass of floor section B is 12 kg, and the sphere bounces back upwards a distance of 44 mm. Knowing that the maximum deflection of the floor section is 33 mm from its equilibrium position, determine (a) the coefficient of restitution between the sphere and the floor, (b) the effective spring constant k of the floor section.Consider a roller-coaster car on a track that has a loop of known radius R. If there is no friction between the rollercoaster car and the track, then determine (a) the minimum speed at the top of the loop for the rollercoaster car to still be in contact with the track and (b) the minimum height h the rollercoaster car must start from in order to go all the way around the loop without losing contact with the track (assuming the rollercoaster starts from rest). The only knowns here are R and g, so your symbolic answers need to be in terms of these. Part (a) can be treated using newton's second law and uniform circular motion (even though it's not really uniform). Start with a free-body diagram of a coaster car at the top of the loop. What does it mean for the rollercoaster car to still be "in contact" with the track? Part (b) can be treated using conservation of mechanical energy. You'll need your result from part (a). How high above the ground are you when you're at the top…A 1.5-kg box is released from rest on a frictionless surface that is sloped at θ = 35◦ above the horizontal.After sliding 1.0 m down the slope, the box transitions smoothly to a rough, horizontal surface, slides forsome distance, and then comes to a stop. If the coefcient of kinetic friction between the box and thehorizontal surface is 0.12, how far along the horizontal surface does the box travel?
- A miniature hill in a child’s toy collection is shown below. When released at A, a mass m slides down the path shown below, reaching the bottom (B) with a speed of vB. Assume that the hill has negligible friction. The block then slides along the rough horizontal surface a distance d before coming to rest at C. When solving parts (a) and (b): Write the useful description about what is known and unknown. Write down the physics principle or strategy you will use. Symbolically solve for the unknowns (a) Calculate the height of the hill using m=230.0 g and vB = 3.8 m/s (b) What is the coefficient of kinetic friction along the horizontal surface if d=14 m? Hint: Treat the motion down the hill and the motion down the rough horizontal surface as two distinct problems. What physics concepts can you apply for each?Let Á = 2.0 m/s i – 9.0 m/s j+5.0 m/s k and let B = 2.0 kg kg j+ 2.0 kg k ,what is A· B?