sphere moves in simple harmonic motion with a frequency of 1.00 Hz and an amplitude of 4.90 cm. What is the maximum magnitude of acceleration (in m/s2) of the sphere? Where in the motion does the maximum acceleration occur?

At time t = 62 s, an oscillator of angular frequency 6.4 s is at position x = -3.8 cm moving at velocity v = 13 cm/s. What is its acceleration at this moment? -140 cm/s? 160 cm/s2 2.4 m/s2 -56 cm/s2 9.8 m/s2

Consider a block and spring system such as shown in Interactive Fig. 15.3.1. The expressions for displacement, velocity, and acceleration of the block are studied in the simulation “Displacement, Velocity, and Acceleration of Simple Harmonic Motion". By default, the amplitude is chosen to be xm 1 m, and the phase angle is chosen to be = π/2 rad. Run the time animation to see the three quantities plotted as a function of time. = oooooooo m x=0 X +xm Interactive Figure 15.3.1: A block of mass m is connected to a spring of spring constant k. The horizontal surface is frictionless.

A particle moves along the x axis. It is initially at the position 0.330 m, moving with velocity 0.250 m/s and acceleration -0.330 m/s2. Suppose it moves with constant acceleration for 3.40 s. We take the same particle and give it the same initial conditions as before. Instead of having a constant acceleration, it oscillates in simple harmonic motion for 3.40 s around the equilibrium position x = 0. Hint: the following problems are very sensitive to rounding, and you should keep all digits in your calculator.   Find its phase constant ϕ0 if cosine is used for the equation of motion. Hint: when taking the inverse of a trig function, there are always two angles but your calculator will tell you only one and you must decide which of the two angles you need. ___________ rad    Find its position after it oscillates for 3.40 s. _______ m   Find its velocity at the end of this 3.40 s time interval. ________ m/s