PHY 101 Chapter Notes - Chapter 13: Intermediate Frequency, Damping Ratio, Arc Length

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Periodic motion: a motion that repeats itself over and over. One of the key characteristics of a periodic system is the time required for the completion of one cycle of its repetitive motion- period. Period (t): time required for one cycle of periodic motion; unit: s. Frequency (f): the number of oscillations per unit of time, the inverse of the period; f= 1/t; unit: 1/s, s-1t. Hertz (hz): a special unit for the measurement of frequency; The smaller the period the larger the frequency. Simple harmonic motion: motion of an object that is repeated oscillations in a period of time t. An example of shm comes with springs; when at equilibrium they are neither stretched no compressed and at position x=0. When a spring is displaced from equilibrium, it exerts a restoring force whose magnitude is proportional to the distance it displaced from equilibrium.

Related Questions

Good Vibes: Introduction to Oscillations

The conditions that lead to simple harmonic motion are as follows:

There must be a position of stable equilibrium.

There must be a restoring force acting on the oscillating object. The direction of this force must always point toward the equilibrium, and its magnitude must be directly proportional to the magnitude of the object's displacement from its equilibrium position. Mathematically, the restoring force F⃗ is given by ⃗, where is the displacement from equilibrium and k is a constant that depends on the properties of the oscillating system.

The resistive forces in the system must be reasonably small.

Consider a block of mass m attached to a spring with force constant k, as shown in the figure(Figure 1) . The spring can be either stretched or compressed. The block slides on a frictionless horizontal surface, as shown. When the spring is relaxed, the block is located at x=0. If the block is pulled to the right a distance A and then released, A will be the amplitude of the resulting oscillations.

Assume that the mechanical energy of the block-spring system remains unchanged in the subsequent motion of the block.

Part A

After the block is released from x=A, it will

(a) remain at rest

(b) move to the left until it reaches equilibrium and stop there.

(d) move to the left until it reaches x=−A and then begin to move to the right.

The time it takes the block to complete one cycle is called the period. Usually, the period is denoted T and is measured in seconds.

The frequency, denoted f, is the number of cycles that are completed per unit of time: f=1/T. In SI units, f is measured in inverse seconds, or hertz (Hz).

Part B

If the period is doubled, the frequency is

(a) unchanged

(b) doubled

Part C

An oscillating object takes 0.10 s to complete one cycle; that is, its period is 0.10 s. What is its frequency f?

Express your answer in hertz.

Part D

If the frequency is 40 Hz, what is the period T?

Express your answer in seconds.

The following questions refer to the figure (Figure 2) that graphically depicts the oscillations of the block on the spring.

Note that the vertical axis represents the x-coordinate of the oscillating object, and the horizontal axis represents time.

Part E

Which points on the x-axis are located at a distance A from the equilibrium position?

(a) R only

(b) Q only

Part F

Suppose that the period is T. Which of the following points on the t-axis are separated by the time interval T?

(a) K and L

(b) K and M

(d) L and N

(e) M and P

Now assume for the remaining Parts G - J, that the x coordinate of point R is 0.12 m and the t coordinate of point K is 0.0050 s.

Part G

What is the period T?

Express your answer in seconds.

Part H

How much time t does the block take to travel from the point of maximum displacement to the opposite point of maximum displacement?

Express your answer in seconds.

Part I

What distance d does the object cover during one period of oscillation?

Express your answer in meters.

Part J

What distance d does the object cover between the moments labeled K and N on the graph?

Express your answer in meters.

emeraldyak680

a).An object of mass 541 g is attached to a spring with springconstant k = 653 N/m. If the object is displaced by 130 mm from theequilibrium position and is released, with what speed doe theobject pass through the equilibrium position during itsmotion?

Express the result in the unit [m/s] and to three significantfigures. If you must use scientific notation, please enter asfollows: e.g. 0.000123 = 1.23E-4. Only answer in numerical values,no units. For negative numbers, leave no space between the negativesign and the number: e.g. right: -1.00, wrong: - 1.00.

b).An object has a mass of m = 647 g. It is attached to a springwhich has a spring constant of value k = 65 N/m. At time t = 0 theobject is pulled to a distance of 28.1 cm from its equilibriumposition (which you may choose conveniently at x = 0). The surfaceon which the object moves is frictionless.

What is the total energy of the system?

Express the result in the unit [J] and to three significantfigures. If you must use scientific notation, please enter asfollows: e.g. 0.000123 = 1.23E-4. Only answer in numerical values,no units. For negative numbers, leave no space between the negativesign and the number: e.g. right: -1.00, wrong: - 1.00.

c).The vibration of the tympanic membrane in the human ear(eardrum) can be described as a harmonic motion. Assuming a mass of20.6 mg and a period of vibration of 1.72 ms, what is the naturalvibration frequency of the membrane?

Express the result in the unit [Hz] and to three significantfigures. If you must use scientific notation, please enter asfollows: e.g. 0.000123 = 1.23E-4. Only answer in numerical values,no units. For negative numbers, leave no space between the negativesign and the number: e.g. right: -1.00, wrong: - 1.00.

d).An object of mass m is attached to a spring with spring constantk = 170 N/m. At time t = 0 the object is pulled to a distance of0.18 m from its equilibrium position. The surface on which theobject moves is frictionless and the spring is within its elasticregime. What is the mass of the object if it oscillates with afrequency f = 2.90 Hz when it is released?

Express the result in the unit [kg] and to three significantfigures. If you must use scientific notation, please enter asfollows: e.g. 0.000123 = 1.23E-4. Only answer in numerical values,no units. For negative numbers, leave no space between the negativesign and the number: e.g. right: -1.00, wrong: - 1.00.

PHY 101 Chapter Notes - Chapter 13: Intermediate Frequency, Damping Ratio, Arc Length

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