1) A silicon cantilever beam with mass = 4 x 10-10 Kg has a spring constant...
1) A silicon cantilever beam with mass = 4 x 10-10 Kg has a spring constant of 31 N/m. Calculate the natural frequency of the beam in Hz. Assume no damping.
2) An atom in a lattice has a resonance frequency of 9.2 THz. According to quantum mechanics, what is the lowest amount of energy this oscillator can have?
Express answer in J.
Homework Answers
Using basic formula of natural frequency we can solve the
problem no. 1 as below- 
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1) A silicon cantilever beam with mass = 4 x 10-10 Kg
has a spring constant...
an atom in a crystal lattice can be regarded as a mass of 2x10^-26 kg attached...
an atom in a crystal lattice can be regarded as a mass of 2x10^-26 kg attached to a spring. The frequency of this oscillator is 1x10^13 Hz. what is the amplitude of oscillation if the energy of oscillation is one energy quantum? Two energy quanta?
A mass of 1.32 kg is connected to a spring of spring constant 8.81 N/m ....
A mass of 1.32 kg is connected to a spring of spring constant 8.81 N/m . An oscillation is started by pulling the mass to the right to amplitude 0.582m before release and the oscillator moves in air. The oscillation decays to 18.2% of the original amplitude in 58.2 seconds. the damping constant of the oscillation is 7.73*10^-2 kg/s total energy has the system lost in this time due to air damping = 1.44 j the amplitude of the oscillation...
6. (12pts) A spring with a mass of 1 kg has damping constant 10 kg/s and...
6. (12pts) A spring with a mass of 1 kg has damping constant 10 kg/s and a spring constant 41 kg/s2. If the spring begins at equilibrium position and is given a velocity of 2 m/s, find the position of the mass at any time t. Is this overdamping, critical damping or underdamping?
A mass-on-a-spring system has a spring constant k = 360 N/m and a mass m =...
A mass-on-a-spring system has a spring constant k = 360 N/m and a mass m = 0.53 kg. (a) If it is given an initial displacement of 0.27 m and then released, what is the initial potential energy of the oscillator? in J (b) What is the maximum kinetic energy of the oscillator? in J
5. A 2 kg mass is attached to a massless spring of force constant k25 N/m....
5. A 2 kg mass is attached to a massless spring of force constant k25 N/m. The spring is stretched 0,40 m from its equilibrium position and released. a. Find the total energy and frequency of oscillation according to classical calculations. b. Determine the quantum number, n, for the system according to quantum calculations. c. How much energy would be carried away in a l-quantum change?
A ball of mass m oscillates on a spring with spring constant k = 200 N/m...
A ball of mass m oscillates on a spring with spring constant k = 200 N/m . The ball's position is described by x=(0.360 m )cos( 16.0 t), with t measured in seconds. A) What is the amplitude of the ball's motion? 0.180 m 16.0 m 8.00 m 0.360 m 0.720 m Part B What is the frequency of the ball's motion? 5.44 Hz 16.0 Hz 6.28 Hz 0.360 Hz 2.55 Hz Part C What is the value of the...
A spring with a mass of 2 kg has a damping constant 14 kg/s. A force...
A spring with a mass of 2 kg has a damping constant 14 kg/s. A force of 3.6 N is required to keep the spring stretched 0.3 m beyond its natural length. The spring is stretched 0.6 m beyond its natural length and then released. Find the position of the mass at any time t. (Assume that movement to the right is the positive x-direction and the spring is attached to a wall at the left end.)
Ignore damping forces. A mass of 4 kg is attached to a spring with constant k- 16 N/m, then the s...
Ignore damping forces. A mass of 4 kg is attached to a spring with constant k- 16 N/m, then the spring is stretched 1 m beyond its natural length and given an initial velocity of 1 m/sec back towards its equilibrium position. Find the circular frequency ω, period T, and amplitude A of the motion. (Assume the spring is stretched in the positive direction.) A 7 kg mass is attached to a spring with constant k 112 N m. Given...
A spring with a mass of 2 kg has a damping constant 14 kg/s. A force of 3.6 N is required to keep...
A spring with a mass of 2 kg has a damping constant 14 kg/s. A force of 3.6 N is required to keep the spring stretched 0.3 m beyond its natural length. The spring is stretched 0.6 m beyond its natural length and then released. Find the position of the mass at any time t. (Assume that movement to the right is the positive x-direction and the spring is attached to a wall at the left end.)
help with 1-3 1) A simple harmonic oscillator consists of a 0.100 kg mass attached to...
help with 1-3
1) A simple harmonic oscillator consists of a 0.100 kg mass attached to a spring whose force constant is 10.0 N/m. The mass is displaced 3.00 cm and released from rest. Calculate (a) the natural frequency fo and period T (b) the total energy , and (c) the maximum speed 2) Allow the motion in problem 1 to take place in a resisting medium. After oscillating for 10 seconds, the maximum amplitude decreases to half the initial...
6. (12pts) A spring with a mass of 1 kg has damping constant 10 kg/s and a spring constant 41 kg/s2. If the spring begins at equilibrium position and is given a velocity of 2 m/s, find the position of the mass at any time t. Is this overdamping, critical damping or underdamping?
5. A 2 kg mass is attached to a massless spring of force constant k25 N/m. The spring is stretched 0,40 m from its equilibrium position and released. a. Find the total energy and frequency of oscillation according to classical calculations. b. Determine the quantum number, n, for the system according to quantum calculations. c. How much energy would be carried away in a l-quantum change?
Ignore damping forces. A mass of 4 kg is attached to a spring with constant k- 16 N/m, then the spring is stretched 1 m beyond its natural length and given an initial velocity of 1 m/sec back towards its equilibrium position. Find the circular frequency ω, period T, and amplitude A of the motion. (Assume the spring is stretched in the positive direction.) A 7 kg mass is attached to a spring with constant k 112 N m. Given...
help with 1-3
1) A simple harmonic oscillator consists of a 0.100 kg mass attached to a spring whose force constant is 10.0 N/m. The mass is displaced 3.00 cm and released from rest. Calculate (a) the natural frequency fo and period T (b) the total energy , and (c) the maximum speed 2) Allow the motion in problem 1 to take place in a resisting medium. After oscillating for 10 seconds, the maximum amplitude decreases to half the initial...
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