The shaking you feel during an earthquake is caused by seismic waves that propagate through the Earth with different speeds, wavelengths, and amplitudes. The type of wave often felt far from the epicenter is the Love wave, where the ground slides back and forth horizontally but not up and down. A crude seismograph records the shaking with a pen attached to a mass (the round thing in the figure above) suspended so that its inertia prevents it from shaking during an earthquake. The ground shakes underneath the pen, and the rolling drum feeds fresh paper for the pen to record the shaking.

(a) The seismograph records a sinusoidal wave with an amplitude of 4.0 cm and a period of 0.83 s. Make an expression for the lateral movement of the ground as a function of time. Write it symbolically and define each variable in the expression. (b) Make an expression for the transverse velocity of the ground as a function of time. What is the maximum horizontal speed of the ground? (c) Make an expression for the transverse acceleration of the ground as a function of time. What is the maximum horizontal acceleration of the ground? (d) The Mercalli scale measures the perceived shaking of earthquakes. This scale is separate from the Richter scale, which measures the strength of earthquakes. How does the earthquake in this problem rank on the Mercalli scale? Note that acceleration is listed in units of g, the gravitational acceleration.