An object with mass m is moving in SHM. It has amplitudeA1 and total mechanical energy E1 when the spring has force constant k1.You want to quadruple the total mechanical energy, so E2 = 4E1, andhalve the amplitude, so A2 = A1/2, by using a different spring, one withforce constant k2. (a) How is k2 related to k1? (b) What effect will thechange in spring constant and amplitude have on the maximum speed ofthe moving object?

A uniform thin rod of length L oscillates as a pendulum about a pivot point that is a distance a from the center. For what value of a, expressed as a fraction of L, is the oscillation period a minimum?

A 2 kg mass attached to a horizontal ideal spring with spring constant k = 8 n2 N/m oscillates in SHM. a) Att = 0, the mass is at x = +0.5 m from its equilibrium position and has a velocity of- 3.0 m/s. Calculate K and U at t = 0 and then find E = K +U, the total mechanical energy of the system. b) From your answer in a), find A, the amplitude of the oscillations c) Find o, the angular frequency. d) Find o, the phase angle in radians from initial conditions by evaluating: x (t) = A cos (@t + 4) and v(t) if x(0) = + 0.5 m and v(0) = - 3 m/s. %3D %3D | %3D %3D

Using conservation of energy, derive a formula for the speed of an object that has a mass M, is on a spring that has a force constant k, and is oscillating with an amplitude of A, as a function of position v(x). (b) If M has a value of 250 g, the spring constant is 85 N/m, and the amplitude is 10.0 cm, use the formula to calculate the speed of the object at x = 0 cm, 2.0 cm, 5.0 cm, 8.0 cm, and 10.0 cm.

A 230.0 g object on a spring oscillates on a frictionless horizontal surface with frequency 2.00 Hzand amplitude 8.0 cm. Its position of time is given by x = Asin(ωt) . A sketch a graph of theelastic potential energy as a function of time. (b) Graph the system’s kinetic energy and potentialenergy as a function of time. (c) Describe qualitatively how your answers would change if thesurface weren’t frictionless.[

A 0.480 kg object connected to a light spring with a spring constant of 19.5 N/m oscillates on a frictionless horizontal surface. The amplitude of motion is 3.00 cm. a) Calculate the total energy of the system (in J). [Select ] b) Calculate the maximum speed of the object (in m/s). [ Select ] c) Find the velocity of the object when the displacement is 2.00 cm (in m/s). [ Select ] d) Find the kinetic energy of the system when the displacement is 2.00 cm (in J). [ Select ] e) Find the potential energy of the system when the displacement is 2.00 cm (in J). [ Select ]

A vertical spring stretches 8.2 cm when a 1.6 kg block is hung from its end. (a) Calculate the spring constant. This block is then displaced an additional 4.8 cm downward and released from rest. Find the (b) period, (c) frequency, (d) amplitude, and (e) maximum speed of the resulting SHM.

Grandfather clocks are designed so they can be adjusted by moving the weight at the bottom of the pendulum up or down. Suppose you have a grandfather clock at home that runs slow by 6 seconds per minute, or 10%. Which of the following adjustment(s) would make it more accurate? (This is a multi-select question. You may select one or more options.) O Decrease the amplitude of swing by 10%. Decrease the length of the pendulum to approximately (0.9)2 times the original length. Take away mass from the weight because the period is inversely proportional to square root of the mass. Increase the length of the pendulum to approximately (1.1)2 times the original length. Add more mass to the weight because the period is proportional to square root of the mass. Increase the amplitude of swing by 10%.

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…

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