4. A helical spring has a stiffness 25000If a mass of 100kg is attached to its free end,pulled down ,and released,determine the period. If the maximum deflection was 50mm ,find the velocity and acceleration of the mass when it is 30mm from the equilibrium position.

14. For the system shown to the right, the disk of mass m rolls without slip and z measures the displaccment of the disk from the unstretchcd position of the spring. 3k a) find the cquations of motion; b) if the system is inderdamped, whiat is the frequency of the frec vibrations of this system in terms of the parancters k, с, and m;

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The wheel is attached to the spring. The mass of the wheel is m=20 kg. The radius of the wheel is 0.6m. The radius of gyration ke=0.4 m. The spring's unstretched length is Lo=1.0 m. The stiffness coefficient of the spring is k-2.0 N/m. The wheel is released from rest at the state 1 when the angle between the spring and the vertical direction is 8-30°. The wheel rolls without slipping and passes the position at the state 2 when the angle is 0=0°. The spring's length at the state 2 is L2=4 m. (4) The elastic potential energy at the potion 1 is_ HULKU 2₂ State 2 G m State 1 (N-m) (two decimal places)

18.37 The radius of the pulley is R 100 mm and its moment stant is k - of inertia is I 0.1 kg-m². The mass m = 5 kg. The spring con- 135 N/m. The system is released from rest with the spring unstretched. What maximum distance does the mass fall before rebounding? Strategy: Assume that the mass has fallen an arbitrary distance x. Write the equations of motion for the mass and the pulley and use them to determine the acceleration a of the mass as a function of x. Then apply the chain rule: dv dt dv dx dv dx dt dx k R m Problems 18.36/18.37

Mass of both blocks = 14kg. The friction coefficient for this bar is µ= 0.4. The spring constant k= 60 N/m. The spring is compressed 0.1 m and then released. d a Find: www 1. The magnitude of block B's acceleration 2. The magnitude of tension of the rope A B a=?

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The disk shown in (Figure 1) has a weight of 10 lb and rolls without slipping on the horizontal surface as it oscillates about its equilibrium position. Figure k = 100 lb/ft 1 of 1 Part A If the disk is displaced, by rolling it counterclockwise 0.4 rad, determine the equation which describes its oscillatory motion when it is released. Initially, the disk is at rest. Express your answer in terms of the variable t. Enter coefficients using three significant figures. 0(t) = Submit Provide Feedback V7 ΑΣΦ Request Answer ↓↑ vec ? Next >

A mass of 250 g stretches a spring 3.828125 cm. If the mass is set in motion from its equilibrium position with a downward velocity of and if there is no damping, determine the position u of the cm 50 2 S mass at any time t. m NOTE: Assume g = 9.8- and enter an exact answer. u(t) When does the mass first return to its equilibrium position? NOTE: Enter an exact answer.. t= S m

Sketch a free body diagram, Apply the principle of work and energy to the system to find the tension in the rope. Please use solve with the method provided only and apply the relevant kinematic equation(s) Keep final answer in lb*ft/s.