A mass is placed on a frictionless, horizontal table. A spring (k = 115 N/m), which can be stretched or compressed, is placed on the table. A 3-kg mass is anchored to the wall. The equilibrium position is marked at zero. A student moves the mass out to x = 7.0 cm and releases it from rest. The mass oscillates in simple harmonic motion. Find the position, velocity, and acceleration of the mass at time t = 3.00 s. x(t = 3.00 s) = 6.73 cm v(t = 3.00 s) -11.96 X cm/s a(t = 3.00 s) = -258.3 o cm/s²

A 0.45 kg block rests on a frictionless horizontal countertop, where it is attached to a massless spring whose k-value equals 19.0 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 x₁ = -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? m/s (b) How fast is the block moving (in m/s) when the spring is momentarily compressed by 1.70 cm (that is, when x = -1.70 cm)? m/s (c) How fast is the block moving (in m/s) whenever the spring is extended by 1.70 cm (that is, when passing through x = +1.70 cm)? m/s (d) Find the magnitude of the displacement (in cm) at which the block moves with one-half of the maximum speed. |x| = cm

A mass is placed on a frictionless, horizontal table. A spring (k=175 N/mk=175 N/m), which can be stretched or compressed, is placed on the table. A 3.5-kg mass is anchored to the wall. The equilibrium position is marked at zero. A student moves the mass out to x=7.0 cmx=7.0 cm and releases it from rest. The mass oscillates in simple harmonic motion. Find the position, velocity, and acceleration of the mass at time t=3.00 st=3.00 s. x(t=3.00 s)=x(t=3.00 s)=  cm v(t=3.00 s)=v(t=3.00 s)=  cm/s a(t=3.00 s)=a(t=3.00 s)=  cm/s2

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…