Homework Answers
The frequency of SHM in spring is determined by the mass and stiffness of the spring
time period = 2pi*sqrt(m/k)
where m = mass
k = spring constant
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. If a body oscillates vertically from a spring, the restoring force has magnitude kx. Therefore...
To understand the use of Hooke's law for a spring. Hooke's law states that the restoring...
To understand the use of Hooke's law for a spring. Hooke's law states that the restoring force F⃗ on a spring when it has been stretched or compressed is proportional to the displacement x⃗ of the spring from its equilibrium position. The equilibrium position is the position at which the spring is neither stretched nor compressed. Recall that F⃗ ∝x⃗ means that F⃗ is equal to a constant times x⃗ . For a spring, the proportionality constant is called the spring constant and denoted...
A 1.5 kg body oscillates in SHM on a spring that, when extended 2.3 mm from...
A 1.5 kg body oscillates in SHM on a spring that, when extended 2.3 mm from its equilibrium position, has an 8.1 N restoring force. What are (a) the angular frequency of oscillation, (b) the period of oscillation, and (c) the capacitance of an LC circuit with the same period if L is 7.6 H?
For my lab a 50g mass is on a spring. The spring is pulled down a...
For my lab a 50g mass is on a spring. The spring is pulled down
a different length for each trial and then released. What would the
amplitude of motion be for this experiment and how can I test that
the frequency is independent from the amplitude.
In cases where the restoring force is proportional to the amount of displacement from the oquilibrium position, the object undergoes simple harmonic motion (SHM). An object on a spring is the simplest example...
Hooke's Law represents a linear restoring force where an elastic system is displaced from equilibrium. In...
Hooke's Law represents a linear restoring force where an elastic system is displaced from equilibrium. In an experiment a rubber band and a spring were placed in a vertical position and a series of having Masses were attached to the free end. a) Does the rubber band used exhibit Hooke's Law behavior? Why or why not? b) Does the spring used exhibit Hooke's Law behavior ? Why or why not? c) Simple Harmonic Motion is oscillatory motion of a system...
Chapter 31, Problem 006 A 2.3 kg body oscillates in SHM on a spring that, when...
Chapter 31, Problem 006 A 2.3 kg body oscillates in SHM on a spring that, when extended 2.4 mm from its equilibrium position, has an 10 N restoring force. What are (a) the angular frequency of oscillation, (b) the period of oscillation, and (c) the capacitance of an LC circuit with the same period if L is 7.1 H? (a) Number (b) Number (c) Number Units Units Units
Problem 2. (6 pts: 2 + 2 + 2) A car oscillates vertically on a bumpy...
Problem 2. (6 pts: 2 + 2 + 2) A car oscillates vertically on a bumpy road as if it were a mass m = 400kg on a spring, with spring constant k = 4 x 10^N/m. The car is moving at a constant velocity v, and at time t, the equation of the road surface below the car is given by ut y(t) = to cos (10) a) Let X(t) be the upward displacement of the mass m from...
Consider a mass m suspended from a massless spring that obeys Hooke's Law (i.e. the force...
Consider a mass m suspended from a massless spring that obeys Hooke's Law (i.e. the force required to stretch or compress it is proportional to the distance stretched/compressed). The kinetic energy T of the system is mv2/2, where v is the velocity of the mass, and the potential energy V of the system is kr-/2, where k is the spring constant and x is the displacement of the mass from its gravitational equilibrium position. Using Lagrange's equations for mechanics (with...
The term oscillator describes any system that has cyclic or near-cyclic behavior. The periodic motion of...
The term oscillator describes any system that has cyclic or near-cyclic behavior. The periodic motion of a planet or a pendulum, the alternating current in an electrical circuit, the vibrations of cesium atoms in an atomic clock are examples of oscillators. It turns out that many oscillators are governed by differential equations- equations that involve a function and its derivatives. In this project we explore solutions of a common oscillator equation. Imagine a block hanging vertically from a spring that...
Engineers have invented a new kind of spring whose restoring force is proportional to the third power of displacement
Engineers have invented a new kind of spring whose restoring force is proportional to the third power of displacement: |F(x)| = |βx3| where B = (1/9) N/m3. One end of this spring is fixed to the bottom of an inclined plane which makes an angle θ = 36.87° with respect to the horizontal, and the other end is stretched up the incline and attached to a block of mass m = 3.00 kg. The spring is initially stretched a distance...
A 2kg mass is suspended vertically from a spring attached to a fixed support. The spring...
A 2kg mass is suspended vertically from a spring attached to a fixed support. The spring satisfies Hooke's law with a spring constant of k 18 N m1. No damping is present. Gravity acts on the mass with a gravitational constant of g 10 m s2. An external force of R 24 sin (wt) Newton is applied to the mass, directed downwards, where t is the time in seconds since the mass was set in motion and w is a...
For my lab a 50g mass is on a spring. The spring is pulled down
a different length for each trial and then released. What would the
amplitude of motion be for this experiment and how can I test that
the frequency is independent from the amplitude.
In cases where the restoring force is proportional to the amount of displacement from the oquilibrium position, the object undergoes simple harmonic motion (SHM). An object on a spring is the simplest example...
Chapter 31, Problem 006 A 2.3 kg body oscillates in SHM on a spring that, when extended 2.4 mm from its equilibrium position, has an 10 N restoring force. What are (a) the angular frequency of oscillation, (b) the period of oscillation, and (c) the capacitance of an LC circuit with the same period if L is 7.1 H? (a) Number (b) Number (c) Number Units Units Units
Problem 2. (6 pts: 2 + 2 + 2) A car oscillates vertically on a bumpy road as if it were a mass m = 400kg on a spring, with spring constant k = 4 x 10^N/m. The car is moving at a constant velocity v, and at time t, the equation of the road surface below the car is given by ut y(t) = to cos (10) a) Let X(t) be the upward displacement of the mass m from...
Consider a mass m suspended from a massless spring that obeys Hooke's Law (i.e. the force required to stretch or compress it is proportional to the distance stretched/compressed). The kinetic energy T of the system is mv2/2, where v is the velocity of the mass, and the potential energy V of the system is kr-/2, where k is the spring constant and x is the displacement of the mass from its gravitational equilibrium position. Using Lagrange's equations for mechanics (with...
The term oscillator describes any system that has cyclic or near-cyclic behavior. The periodic motion of a planet or a pendulum, the alternating current in an electrical circuit, the vibrations of cesium atoms in an atomic clock are examples of oscillators. It turns out that many oscillators are governed by differential equations- equations that involve a function and its derivatives. In this project we explore solutions of a common oscillator equation. Imagine a block hanging vertically from a spring that...
A 2kg mass is suspended vertically from a spring attached to a fixed support. The spring satisfies Hooke's law with a spring constant of k 18 N m1. No damping is present. Gravity acts on the mass with a gravitational constant of g 10 m s2. An external force of R 24 sin (wt) Newton is applied to the mass, directed downwards, where t is the time in seconds since the mass was set in motion and w is a...
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