A mass of 5 kg stretches a spring 10 cm. The mass is acted on by an external force of 10 sin t 4 N (newtons) and moves in a medium that imparts a viscous force of 2 N when the speed of the mass is 2 cm/s. If the mass is set in motion from its equilibrium position with an initial velocity of 7 cm/s, formulate the initial value problem describing the motion of the mass. (Use g = 9.8 m/s2 for the acceleration due to gravity. Let u(t), measured positive downward, denote the displacement in meters of the mass from its equilibrium position at time t seconds. Use up for u' and upp for u''.)

Acar accelerates from 5.0 m/s to to 11 m/s at a rate of 3.0 m/s^2. how far does it travel while accelerating? 20m 117m 43m 16m

Scientists use laser range-finding to measure the distance to the moon with great accuracy. a brief laser pulse is fired at the moon, then the time interval is measured until the "echo" is seen by a telescope. a laser beam spreads out as it travels because it diffracts through a circular exit as it leaves the laser. in order for the reflected light to be bright enough to detect, the laser spot on the moon must be no more than 1.0 km in diameter. staying within this diameter is accomplished by using a special large-diameter laser. part a if λ = 540nm , what is the minimum diameter of the circular opening from which the laser beam emerges? the earth-moon distance is 384,000 km. express your answer to two significant figures and include the appropriate units.

In a stagnant pool of water, a crayfish may spend much of its time lying with one side of its carapace near the surface of the water. in this position, it will move the walking legs on that side in a rhythmic back-and-forth motion. explain the likely function of this behavior.