Nonlinear springs are classified as hard or soft, depending upon the curvature of their force-deflection curve (see figure). If a delicate instrument having a mass of 5 kg is placed on a spring of length / so that its base is just touching the undeformed spring and then is inadvertently released from that position, determine the maximum deflection xm of the spring and the maximum force Fm exerted by the spring, assuming (a) a linear spring of constant
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- A rigid block of mass M is mounted on four elastic supports, as shown in the figure below. A small mass m drops from a height h and adheres to the rigid block without rebounding, and the spring constant of each elastic support is k. Determine the equation of motion of the system after the small mass strikes the block. Given the following values, if the equation of motion is in the form + az = 0, determine the value of a. M = 55 kg; m = 6 kg; k=181 N/m; h= 20 cm a = Hence, determine the natural frequency of vibration of the system in units, Hz. f= The springs are modified, so that the equation of motion is now +14x=0. If x = 0 at the static equilibrium position when both masses are included, the initial position is given by mg 20. Hence, determine the initial velocity of the system at the point of impact, ż (t = 0) = V₁ (units m/s). Vo = If the resulting motion of the system after the impact is of the form r(t) = A cos wnt + B sin wnt, determine the values, A = B= wn (rad/s) = k k M m h…arrow_forward2. A spring is hung vertically and an object of mass m attached to the lower end is then slowly lowered a distance d to the equilibrium point a. find the value of the spring constant if the magnitude of the displacement d is 2.0 cm and the mass is .55 kg b. if a second identical spring is attached to the object in parallel with the first spring, where is the new equilibrium point of the system? c. What is the effective spring constant of the two springs acting as one?arrow_forwardA simple pendulum of mass m and length b moves horizontally with x=a*sin(wt) at its support. Obtain the pendulum's langrange and hamilton equations of motionarrow_forward
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- A block of mass m = 1.2Kg is on a plane %3D inclined at 30 degrees for which uc = 0.11. The block is connected to a spring of constant K = 3.2 N / m, by a rope passing, without slipping, by a pulley. The pulley is a disc of 0.8Kg and 0.14m radius. If the system is initially at rest and the spring has zero elongation, what is the block velocity modulus when the block has slid 0.25m down the inclined plane? k=3,2 N/m 130° A Figure 11.75arrow_forward3. A box of mass m=15 kg at the packaging section of a factory comes to the top of a (0=37°) with speed vo and slides down where it is picked up for shipment. In order to avoid damage to the box a spring is used with force constant k=100N/m and the ramp maximum force Fmax=100N. The box slides a distance of -4 m down the incline before it hits the spring is 0.75. ramp as shown. The coefficient of kinetic friction between the box and entire a) Find the work done by the normal force and Vo gravity friction force on the box until it hits the spring. b) Find the maximum speed of the box at the top of the ramp if the box is to be picked up in the spring is www when maximum compression.arrow_forwardBlock A rests on a horizontal tabletop. A light horizontal rope is attached to it and passes over a pulley, and block B is suspended from the free end of the rope. The light rope that connects the two blocks does not slip over the surface of the pulley (radius 0.080 m) because the pulley rotates on a frictionless axle. The horizontal surface on which block A (mass 2.50 kg) moves is frictionless. The system is released from rest, and block B (mass 5.00 kg) moves downward 1.80 m in 2.00 s. A)What is the tension force that the rope exerts on block B ?B)What is the tension force that the rope exerts on block A ?arrow_forward
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