2. Consider a particle undergoing simple harmonic motion. The velocity of the particle at position x¹ is v¹ and velocity of the particle at position x² is ². Show that the ratio of time period and amplitude is: TA T 21

A hole is drilled through the center of the earth. The gravitational force on a mass in that hole is mgr/R, where r is the distance of the mass from the earth’s center and R is the radius of the earth (6.4 x 10 6m).A mass dropped into the hole executes simple harmonic motion. Find the period of the motion. How does one-half this time compare with the time needed to fly in an air-’ plane halfway around the earth?

An object is attached to a coiled spring. The object is pulled down (negative direction from the rest position) 9 centimeters, and then released. Write an equation for the distance d of the object from its rest position, after t seconds if the amplitude is 9 centimeters and the period is 6 seconds. The equation for the distance d of the object from its rest position is (Type an exact answer, using z as needed. Use integers or fractions for any numbers in the equation.) (? Enter your answer in the answer box. Save for Later 3:18 PM O Type here to search O 11/15/2020 PgUp PgDn F12 DII PrtScn Home F9 End F10 F11 Ins F4 F5 F6 F7 F8 F1 F2 F3 2$ & ) %23 %3D 3. 4. 5 6 7 8 E R Y U | [ T

5 kilogram object is suspended from a string. The string is 4 meters long. What is the period of the object ting as a pendulum? Express your answer a number of seconds, omitting the unit.