When a 0.20-kg block is suspended from a vertically hanging spring, it stretches the spring from its original length of 0.050 m to 0.060 m. The same block is attached to the same spring and placed on a horizontal, frictionless surface. 0.20 kg ww The block is then pulled so that the spring stretches to a total length of 0.10 m. The block is released at time t = 0 and undergoes simple harmonic motion. Complete the following statement: In order to increase the frequency of the motion, one would have to O decrease the mass of the block on the end of the spring. O reduce the spring constant. O increase the distance that the spring is initially stretched. O reduce the distance that the spring is initially stretched.

A 0.60 kg block rests on a frictionless horizontal surface, where it is attached to a massless spring whose k-value equals 18.5 N/m. Let x be the displacement, where x = 0 is the equilibrium position and x > 0 when the spring is stretched. The block is pushed, and the spring compressed, until x, = -4.00 cm. It then is released from rest and undergoes simple harmonic motion. (a) What is the block's maximum speed (in m/s) after it is released? 1.23 X Mechanical energy is conserved in this system, and the gravitational term remains unchanged (since all motion is horizontal). Write an expression for mechanical energy that includes the kinetic energy and the potential energy of the spring. Which term(s) can be ignored when the spring is compressed and the block at rest? Which term(s) can be ignored when the block is moving at its greatest speed? Use the remaining terms, and the given quantities, to solve for the maximum speed. m/s (b) How fast is the block moving (in m/s) when the spring is…

Two massless springs with spring constants 610 N/m and 116 N/m are hung from a hor- izontal support. A block of mass 6 kg is suspended from the pair of springs, as shown. When the block is in equilibrium, each spring is stretched an additional Ar. Then the block oscillates with an amplitude of 49 m and it passes through its equilibrium point with a speed of 539 m/s. 610 N/m -oooo² 6 kg -0000² 116 N/m What is the angular velocity of this system? The acceleration due to gravity is 9.8 m/s. 1. w = 15 2. w = 2 3. w = 11 rad/s 4. w = 13 5. w = 21 6. w = 16 7. w = 8 X 8. w = 4 9. w = 6 10. = 18

A spring hangs vertically from a ceiling. The spring constant of the spring is k=15 N/m. A 2kg object has been attached to the spring and the spring has already come to its new equilibrium. Someone pulls the object down by 5cm and releases it at time t = 0s. The spring and object begin to oscillate under simple harmonic motion. Find the total energy of the system, the maximum kinetic energy, the maximum potential energy, and the positions where the maximum energies occur.  Answers: 0.01875 J, 0.01875 J