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28 Nov 2019

We know that if A is doubled then distance is doubled. Where mass of the object is constant and k is the spring constant, then the Period is independent of amplitude. Further, if A is doubled then max speed will be doubled. OK? But how do I put this together in a relationship...how do I state what is going on?

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16 Feb 2023

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Related questions

A pendulum makes 28 oscillations in exactly 50 s. What is its:

(a) Period?

(b) frequency?

An object with mass 2.7 kg is executing simple harmonic motion, attached to a spring with spring constant k = 310 N/m. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s.

(a) Calculate the angular speed

(b) Calculate the period

cerisehare923

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 horizontal spring with a spring constant of 20.0 N/m is attached to a 0.750 kg mass on a horizontal, frictionless table. The mass is pulled until the spring is stretched to 10.0 cm, then released at time t = 0 s.

a. What is the angular frequency, frequency, and period of the oscillation?

b. What is the amplitude of the motion?

c. At what time will the mass first pass the equilibrium position?

d. At what position is the block after 1.00 seconds?

e. How fast is it going when it passes the equilibrium position?

f. How fast is it going at 2.00 seconds?

g. How fast is it going when it is at the halfway point to the equilibrium position?

h. At what position is it going 0.250 m/s?

i. What is the total mechanical energy of the block?

j. At what position is the energy evenly split between kinetic and spring potential energy?