A wire 0.5 m long and mass 5 × 10³ kg is stretched such that its fundamental frequency of transverse vibration is 100 Hz. Find the tension in the wire. How will you double the frequency by changing the vibrating length ?
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A: Given:- Oscillator frequency f = 130 Hz linear density μ = 0.8 g/m…
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Q: a) What mass m allows the oscillator to set up the fourth harmonic on the string? b) What standing…
A: Solution: Given: L = length of string = 1.5 m n = number of harmonic = 4 μ = mass per unit length of…
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A: The given values are, f=9.19×109 Hzm=2.207×10-25 kgA=3.34×10-10 m
Q: In the figure, a string, tied to a sinusoidal oscillator at P and running over a support at Q, is…
A: Solution: Given: L = length of string = 1.5 m n = number of harmonic = 4 μ = mass per unit length of…
Q: 3. A 150 g toy is undergoing SHM on the end of a horizontal spring with force constant of 300.0 N/m.…
A: Note:- The total energy is the sum of the kinetic and potential energies TE=KE+PE.…
Q: A bullet of mass m= 103.4 Grams has a velocity of v0= 62 m/s just before it strikes the target of…
A: mass of bullet m =103.4 g = 0.1034kg vo = 62 m/s mass of target M=4 kg k =1,326 N/m
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A: We know from Hookes Law : F=-KxAnd Angular Frequency is given by :ω=KM
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- Two 1.3 kg masses and three identical springs having a k value of 85 N/m are connected as demonstrated in the lecture notes. What are the frequencies of the two longitudinal vibration modes?A string has length 2.0 m, tension 60 N, and linear density 0.080 kg/m. The left end of the string is connected to a massless ring that slides on a frictionless pole, and the ring is attached to a spring of stiffness 150 N/m. The right end is attached to a massless ring that slides on a frictionless pole. The left end of the string is driven by a transverse force of amplitude 4.0 N and frequency 21 Hz. F(t) S x = 0 x = L 2. The input mechanical impedance (at x = 0) is Zmo = s/im + ipLc tan(kL). Using established impedances (do not calculate), explain why the input impedance is given by this expression. Evaluate the impedance for the specified values of the system. Be sure to show the units. Note: In the computation of the tangent, do not round off the value of k. From the value of the impedance, determine the steady-state velocity amplitude (in m/s) of the left ring.The midpoint of a guitar string executes simple harmonic motion with motion following the form x(t) = A sin(wt + p). It has an angular frequency of w = 2.65 × 10³ s-¹ and an amplitude of A = 1.50 mm. Take the phase constant to be p = π/2.
- In the figure, a string, tied to a sinusoidal oscillator at P and running over a support at Q, is stretched by a block of mass m. Separation L = 0.8 m, linear density μ = 1.6 g/m, and the oscillator frequency f = 200 Hz. The amplitude of the motion at P is small enough for that point to be considered a node. A node also exists at Q.(a) What mass m allows the oscillator to set up the fourth harmonic on the string?(b) What standing wave mode, if any, can be set up if m = 4 kg (Give 0 if the mass cannot set up a standing wave)?A 0.60 kg block rests on a frictionless horizontal surface, where it is attached to a massless spring whose k-value equals 18.5 N/m. Let x be the displacement, where x = 0 is the equilibrium position and x > 0 when the spring is stretched. The block is pushed, and the spring compressed, until x, = -4.00 cm. It then is released from rest and undergoes simple harmonic motion. (a) What is the block's maximum speed (in m/s) after it is released? 1.23 X Mechanical energy is conserved in this system, and the gravitational term remains unchanged (since all motion is horizontal). Write an expression for mechanical energy that includes the kinetic energy and the potential energy of the spring. Which term(s) can be ignored when the spring is compressed and the block at rest? Which term(s) can be ignored when the block is moving at its greatest speed? Use the remaining terms, and the given quantities, to solve for the maximum speed. m/s (b) How fast is the block moving (in m/s) when the spring is…A 0.250 kg mass is hanging motionless attached to a spring of spring constant 12.0 N/m, one end of which is attached to a rigid support. The mass is pulled down 15.0 cm from its equilibrium position and is given an initial velocity of 1.60 m/s directed toward the equilibrium position. (a) Determine the amplitude of the resulting simple harmonic motion. (b) What is the speed of the mass when it passes through the equilibrium position?
- The motion of a rail car is recorded and found to have an overall grms level of 0.23 Grms. This data is used to reproduce the motion in the lab on a random vibration table. What grms level would the PSD profile need to be scaled to for simulation of a 10 hour train ride in 3 hours in the lab?A 0.417 kg mass is attached to a string with a force constant of 53.9 N/m. The mass is displaced 0.286m from equilibrium and released. Assuming SHM for the system. Part A: With what frequency does it vibrate ? Part B: What is the speed of the mass when it is 0.143m from equilibrium? Part C: What is the total energy stored in this system? Part D: What is the ratio of the kinetic energy to the potential energy when it is at 0.143m from equilibrium?(a) A pendulum is made from a 40 g mass hanging on a 50 cm long string. The pendulum oscillates with a frequency of 0.70 Hz and an amplitude of 10 degrees. (i) If the mass is doubled to 80 g, what would the new frequency be? (ii) If the string length is doubled to 100 cm, what would the new frequency be? (iii) If the amplitude is doubled to 20 degrees, what would the new frequency be?
- A spring-mass system consists of a mass m = 4.0 kg and spring with spring constant k = 145 N/m. %3D What length of simple pendulum would have the same frequency?We can model a molecular bond as a spring between two atoms that vibrate with simple harmonic motion.The figure below shows an simple harmonic motion approximation for the potential energy of an HCl molecule.This is a good approximation when E < 4 ×10^−19. Since mH << mCl, we assume that the hydrogen atomoscillates back and forth while the chlorine atom remains at rest. Estimate the oscillation frequency of theHCl molecule using information in the figure below.A vertical wire 2.1m long and of 0.0042 cm2 cross sectional area has a Young’s modulus of 2.00 x 1011 Pa. A 4.0 kg object is fastened to its end and stretches the wire elastically. If the object is now pulled down a little and released, the object undergoes vertical single harmonic motion. Find the period of its vibration.