# Springs: Simple Harmonic Motion

• TJC747
In summary, the conversation discusses the mass and spring constant of a compact car with four identical springs. The car bounces at a frequency of 2.0 times per second when empty and will have a different oscillation frequency when carrying four 110 kg passengers. The equations for this problem include Hooke's laws, which are relevant for calculating the spring constant. However, the exact equations to use are not mentioned and further assistance is needed.
TJC747
A compact car has a mass of 1050 kg. Assume that the car has one spring on each wheel, that the springs are identical, and that the mass is equally distributed over the four springs.

(a) What is the spring constant of each spring if the empty car bounces up and down 2.0 times each second?
(in N/m)

(b) What will be the car's oscillation frequency while carrying four 110 kg passengers?
(in Hz)

I know all the equations for this problem, most centrally Hooke's laws; however, I am having difficulty piecing them all together. Help would be appreciated. Thanks.

List the equations you know. Which have quantities that are given in the questions?

(a) The spring constant can be calculated using the equation: k = (4π^2m)/T^2, where m is the mass of the car and T is the time for one complete oscillation. In this case, the time for one complete oscillation is 0.5 seconds (since the car bounces up and down 2.0 times each second). Therefore, the spring constant for each spring would be: k = (4π^2 * 1050 kg)/(0.5 s)^2 = 167,400 N/m.

(b) When the car is carrying four 110 kg passengers, the total mass of the car would be 1050 kg + (4*110 kg) = 1490 kg. Using the same equation as above, the oscillation frequency would be: f = 1/T = 1/(2π√(m/k)) = 1/(2π√(1490 kg/167,400 N/m)) = 1.05 Hz.

## 1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position and acts in the opposite direction to the displacement.

## 2. How does a spring exhibit simple harmonic motion?

A spring exhibits simple harmonic motion when it is stretched or compressed from its equilibrium position. The force exerted by the spring is directly proportional to the displacement from the equilibrium position, and this force acts in the opposite direction to the displacement, causing the spring to oscillate back and forth.

## 3. What is the equation for the period of a spring's simple harmonic motion?

The equation for the period of a spring's simple harmonic motion is T = 2π√(m/k), where T is the period in seconds, m is the mass of the object attached to the spring, and k is the spring constant, which is a measure of the stiffness of the spring.

## 4. How does the amplitude affect the motion of a spring?

The amplitude, which is the maximum displacement from the equilibrium position, affects the motion of a spring by determining the maximum potential energy and maximum kinetic energy of the system. A larger amplitude results in a longer period and a greater distance traveled by the object attached to the spring.

## 5. What factors can affect the frequency of a spring's simple harmonic motion?

The frequency of a spring's simple harmonic motion can be affected by the mass of the object attached to the spring, the spring constant, and the amplitude of the motion. A larger mass or spring constant will result in a lower frequency, while a larger amplitude will result in a higher frequency.

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