Answered: 1. Music. When a person sings, his or… | bartleby

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1. Music. When a person sings, his or her vocal cords vibrate in a repetitive pattern
that has the same frequency as the note that is sung. If someone sings the note B
flat, which has a frequency of 466 Hz, how much time does it take the person's vocal
cords to vibrate through one complete cycle, and what is the angular frequency of the
cords?

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2. An object whose mass is 520 g is fastened to the end of a horizontal spring whose spring constant is 78 N/m. The object is pulled 5.0 cm from equilibrium and released. Assume no friction between the object and the floor. (a) What is the angular frequency and the period of oscillation? b) Write the specific equation of motion for this oscillating system, in the form x(t) A cos(cot + )
A mass of 0.340kg oscillates up and down on a spring with a spring constant 45.0 N/m. What is the angular frequency of this motion?
3. The physical pendulum. (a) In class, we derived the formula for the frequency of the physical pendulum W3 Mgl I (1) Show that the expression for the frequency of the simple pendulum is consistent with this. Then derive (1) using the energy method, where the total energy is the sum of the rotational kinetic energy 1/1 (do/dt) 2 and the potential energy of the centre of mass mghem. To obtain the result you will need to use the small angle expression for cosine: cos 01-02/2, for 0 < 1. (b) A thin square plate of side L and mass M is hanging from a pivot that is drilled into one of its corners. The pivot passes perpendicularly through the plate. The plate is then lightly tapped and starts to undergo small oscillations. Using the energy method, determine the period of the oscillation, making the small angle approximation. The moment of inertia for an axis running through the centre of a square plate is ICM ML²/6. =
5. A block is attached to a horizontal spring. Find a model for the displacement d as a function of time given the following conditions: a. At time t = 0, the block is pulled to the left 6 cm with a frequency of 2 Hz. W -3-2-1 0 1 2 3 + d b. At time t = 0, the initial displacement is 0 inches (moving to the right), the amplitude is 15 centimeters, and the period is 1 sec.
Q9
40. The position of a 300.0 g mass attached to a certain spring is given by x = 0.20 sin(5.0t), where x is in meters and t is in seconds. (To graph or calculate use radian mode.) The 5.0 in the equation represents the “angular frequency” and, with units, is: ω = 5.0 radians/second. (Angular frequency satisfies either of these equations: ω = 2πf or ω = 2π/T.) (a) Determine the spring constant k. (b) Determine the maximum amount of force acting on the 300 g mass. (c) Determine a new position function if the original mass is replaced by a 600.0 g object (attached to the same spring) and released from a position of x = 0.30 m at t = 0.0. (Hint: using a cosine function is convenient this time.)
5. An object is attached to a spring and completes only one cycle (i.e. goes back and forth and stops). The object reaches its maximum velocity after 0.250 seconds of motion. Calculate the its angular frequency and the spring constant if the object is 0.125 kg.