Simple Harmonic Motion (SHM) question check

In summary, Simple Harmonic Motion (SHM) is a type of periodic motion that involves an object oscillating back and forth around a stable equilibrium position. It is characterized by a restoring force that is directly proportional to the displacement from the equilibrium position. The key components of SHM are amplitude, period, frequency, and equilibrium position. Unlike other types of motion, SHM involves a restoring force that always points towards the equilibrium position. The equation for SHM is x = A*cos(ωt), and some real-life examples include the motion of a pendulum, a mass on a spring, and a guitar string.
  • #1
saraht4bysion
1
0

Homework Statement


A metal sphere of mass 0.20kg is hung from a helical spring whose top end is clamped. the sphere is displaced by 0.030m below its equilibrium position, and then released. 20 cycles of oscillation, of amplitude 0.030m, occur in a time of 12.0s.
calculate;
(I) the spring stiffness, k. (force per unit extension)
(II) the maximum velocity of the sphere as it oscillates.
(III) the maximum acceleration of the sphere as it oscillates.


Homework Equations


ω=2*∏/T

The Attempt at a Solution


my workings;
(I) W=2*∏/T
=2*∏/1.67
W= 3.76rads-1

w^2=m/k
3.76^2=0.20/k
k=0.20/3.76^2
= 0.20/14.14
k=1.41*10^-2 Nm-1

(II) Vmax= +- W √A^2 - x^2
but x=0 so
Vmax= +- WA
= +- 3.79 * 0.030
Vmax= +- 1.13*10^-1 ms-1

(III) amax= +- W^2 * x
but x=A so
amax= +- W^2 * A
= +- 3.76^2 8 0.030
amax= +- 4.24*10^-1 ms-2

could you please check my answers for me, because, i don't know why, i just feel like I've gone wrong somewhere.
thanks sarah x
 
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  • #2
Welcome to PF;

(I) Reasoning looks OK.
How did you calculate T=1.67(s?)
In 12 seconds you get 20 cycles - how much time for one cycle?

Usually better to combine equations before putting the numbers in - to avoid rounding errors.

(II) and (III) OK reasoning ... you should keep the direction (+/-) since they ask for "velocity" rather than speed.
 

1. What is Simple Harmonic Motion (SHM)?

Simple Harmonic Motion (SHM) is a type of periodic motion in which an object moves back and forth around a stable equilibrium position, following a sinusoidal pattern. This type of motion is characterized by a restoring force that is directly proportional to the displacement from the equilibrium position.

2. What are the key components of SHM?

The key components of SHM are amplitude, period, frequency, and equilibrium position. Amplitude is the maximum displacement from the equilibrium position, while period is the time it takes for one complete oscillation. Frequency is the number of oscillations per unit time, and equilibrium position is the central point around which the object oscillates.

3. How is SHM different from other types of motion?

SHM is different from other types of motion because it involves a restoring force that always points towards the equilibrium position, causing the object to oscillate around that point. Other types of motion may involve forces that do not necessarily point towards a stable equilibrium position.

4. What is the equation for SHM?

The equation for SHM is x = A*cos(ωt), where x is the displacement from the equilibrium position, A is the amplitude, ω is the angular frequency, and t is time. This equation represents a sinusoidal motion with a period of T=2π/ω and a frequency of f=1/T.

5. What are some real-life examples of SHM?

Some real-life examples of SHM include the motion of a simple pendulum, a mass on a spring, and the motion of a guitar string. SHM can also be observed in the motion of a swinging door, a diving board, or a child on a swing.

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