A string attached to an oscillator at one end forms 5 nodes (counting the two ends) and produces a frequency of ν = 3.5 kHz. The string is L = 0.95 m long and is under a tension of T = 297 N.   What is the linear density of the string, in kilograms per meter?

A small fly of mass 0.8 g is caught in a spider's web. The web oscillates predominantly with a frequency of 10 Hz. At what frequency (in Hz) would you expect the web to oscillate if an insect of mass 0.5 g were trapped? (What equation can I use to find the frequency at which it ocilates?)

A spring is hanging down from the ceiling, and an object of mass m is attached to the free end. The object is pulled down, thereby stretching the spring, and then released. The object oscillates up and down, and the time T required for one complete up-and-down oscillation is given by the equation T = 2л√/m/k, where k is known as the spring constant. What must be the dimension of k for this equation to be dimensionally correct? O [T] O [T]² O [M] O [M]/[T] O [T]/[M] O [M]/[T]² O [T]²/[M]

A magnesium atom (mass ≈≈ 24 proton masses) in a crystal is measured to oscillate with a frequency of roughly 1014 Hz. What is the effective spring constant of the forces holding the atom in the crystal?

Problem 2:  Special sections of roadway are sometimes paved with “rumble strips” to alert inattentive drivers. In a particular case the grooves are spaced L = 0.26 m apart and the depth of each groove is d = 0.35 cm. As you drive over this rumble strip, the tires of your car oscillate about their equilibrium positions with a frequency of f = 68.6Hz. Refer to the figure, which is not drawn to scale.  Part (b) Find the vertical position of the tire, in centimeters, at the time t = 1.85 s. Part (c) With your tire oscillating at a frequency of f = 68.6 Hz and the distance between grooves L = 0.26 m, what is the speed of your car, in kilometers per hour?

A light balloon filled with helium of density 0.179 kg/m³ is tied to a light string of length L = 5.45 m. The string is tied to the ground, forming an "inverted" simple pendulum (shown in (a) of following figure). Air a 100->> L He Air L He i Determine the period of the motion (in s). Take the density of air to be 1.18 kg/m³. (Hint: Use an analogy with the simple pendulum. Assume the air applies a buoyant force on the balloon but does not otherwise affect its motion.)

A pendulum has a period of 5.8 s.  If you were to transfer this pendulum to the surface of Mars (where g is 3.71 meters per second squared), what would the period (in seconds) be?

A cubic meter (1.00 m^3) of water with bulk modulus 2.2x10^9 Pa is collected from the ocean's surface, where the atmospheric pressure is 1.0x10^5 Pa. It is brought 10.9 km below the surface in a container that can freely expand/contract, to the bottom of the Marianas Trench where the pressure 1.16x10^8 Pa. What is the volume of the water at this depth?

A pendulum is constructed from a light string of length l=100 cm and a heavy mass m=100 kg . What is the period of the pendulum for small displacements?

A string with a mass m = 8 g and a length L = 5 m has one end attached to a wall, the other end goes over a small massless pulley. At the other side of the pulley, an object with mass M = 6 kg is attached. The length of the string between the wall and the pulley, is d = 4m. a) What is the linear mass density of the string, μ ? b) If the string is plucked, what is the fundamental frequency of its vibration? c) If we change the string with another one having the linear mass density double than the first one (but the same length), what should be the mass of the attached object so that the fundamental frequency is the double of its previous value?