1980M1. A small mass m1 rests on but is not attached to a large mass M2 that slides on its base without friction.
The maximum frictional force between m1 and M2 is f . A spring of spring constant k is attached to the large mass M2 and to the wall as shown above.
a. Determine the maximum horizontal acceleration that M2 may have without causing m1 to slip.
b. Determine the maximum amplitude A for simple harmonic motion of the two masses if they are to move together, i.e., m1 must not slip on M2.
c. The two-mass combination is pulled to the right the maximum amplitude A found in part b. and released. Describe the frictional force on the small mass m1 during the first half cycle of oscillation.
d. The two-mass combination is now pulled to the right a distance of A′ greater than A and released.
i. Determine the acceleration of m1 at the instant the masses are released.
ii. Determine the acceleration of M2 at the instant the masses are released.