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portillo (gdp347) – oldmidterm4 01 – Turner – (58185) 1 This print-out should have 21 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A mass attached to a spring executes sim- ple harmonic motion in a horizontal plane with an amplitude of 1 . 01 m. At a point 0 . 7171 m away from the equilibrium, the mass has speed 2 . 33 m / s. What is the period of oscillation of the mass? Consider equations for x ( t ) and v ( t ) and use sin 2 + cos 2 = 1 to calculate ω . An- swer in units of s. 002 10.0 points A block of unknown mass is attached to a spring of spring constant 6 . 7 N / m and under- goes simple harmonic motion with an ampli- tude of 14 . 1 cm. When the mass is halfway between its equilibrium position and the end- point, its speed is measured to be 33 . 1 cm / s. Calculate the mass of the block. Answer in units of kg. 003 10.0 points A hoop ( i.e. , a ring) of radius 6 . 9 m and mass 5 . 8 kg is suspended from a pivot on the perimeter of the hoop as shown in the figure. The acceleration of gravity is 9 . 8 m / s 2 . x y θ Find the angular frequency ω of small os- cillations. Answer in units of rad / s. 004 10.0 points A 0 . 46 kg mass is attached to a spring and undergoes simple harmonic motion with a pe- riod of 0 . 592 s. The total energy of the system is 2 . 4 J. Find the amplitude of the motion. Answer in units of m. 005 10.0 points Earthquakes produce two kinds of seismic waves: The longitudinal primary waves (called P waves) and the transverse secondary waves (called S waves). Both S waves and P waves travel through Earth’s crust and mantle, but at different speeds; the P waves are always faster than the S waves, but their exact speeds depend on depth and location. For the pur- pose of this exercise, we assume the P wave’s speed to be 8680 m / s while the S waves travel at a slower speed of 4140 m / s.
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