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A 10 g particle undergoes simple harmonic motion with an amplitude of 2.0 mm, a maximum acceleration of 8 x 10\(^3\) m/s\(^2\) , and an unknown phase constant. What are
A. the period of the motion?
B. the maximum speed of the particle?
C. the total mechanical energy of the oscillator?
D. the magnitude of the force on the particle at its maximum and half its maximum displacement?
A block of mass M, 5.4 kg, at rest on a horizontal frictionless table is attached to a rigid support by a spring constant k, 6000 N/m. A bullet of mass m, 9.5 g, and velocity of magnitude 630 m/s strikes and is embedded in the block. Assuming the compression of the spring is negligible until the bullet is embedded, determine:
A. the speed of the block immediately after the collision
B. the amplitude of the resulting simple harmonic motion
An ideal spring is hung from the ceiling and a pan of mass M is suspended from the end of the spring, stretching it a distance D as shown above. A piece of clay, also of mass M, is then dropped from a height H onto the pan and sticks to it. Express all algebraic answers in terms of the given quantities and fundamental constants.
A. Determine the speed of the clay at the instant it hits the pan
B. Determine the speed of the pan just after the clay strikes it
C. Determine the period of the simple harmonic motion that ensues
D. Determine the distance the spring is stretched from its initial unstretched length at the moment the speed of the pan is a maximum.
E. The clay is now removed from the pan and the pan is returned to equilibrium at the end of the spring. A rubber ball, also of mass M, is dropped from the same height H onto the pan, and after the collisions is caught in mid air before hitting anything else. Indicate whether the period of the resulting simple harmonic motion of the pan is greater than, less than, or the same as it was in part (C).