The suspension system in a car includes a spring attached to each wheel as shown - Edexcel - A-Level Physics - Question 16 - 2023 - Paper 2

To find the stiffness (k) of the spring, we can use Hooke's Law, which states that the force (F) is equal to the stiffness (k) multiplied by the extension (x). The weight of the car is given by:

$F = mg = 1100 ext{ kg} imes 9.81 ext{ m/s}^2 = 10891 ext{ N}$

Since each spring supports a quarter of the car's weight:

$F_{spring} = \frac{10891}{4} = 2722.75 ext{ N}$

The compression of each spring (x) is 0.152 m. Thus,

$k = \frac{F_{spring}}{x} = \frac{2722.75 ext{ N}}{0.152 ext{ m}} \approx 17989.84 ext{ N/m} \approx 18000 ext{ N/m}$

For simple harmonic motion, the frequency (f) can be determined using the formula:

$f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}$

Where:

• k (stiffness) is approximately 18000 N/m
• m (mass of the car) = 1100 kg

Using the mass that is additionally compressed:

• The effective mass for oscillation can be taken as the mass supported by each spring, which is:

$m_{eff} = \frac{1100}{4} = 275 ext{ kg}$

Now, substituting the values:

$f = \frac{1}{2\pi} \sqrt{\frac{18000}{275}} \approx \frac{1}{2\pi} \sqrt{65.45} \approx \frac{1}{2\pi} \times 8.08 \approx 1.29 ext{ Hz}$

The conditions for simple harmonic motion include:

1. The acceleration is directly proportional to the displacement from the equilibrium position.
2. The acceleration is always directed towards the equilibrium position.
3. The motion must be periodic.

Using oil of high viscosity will produce heavy damping because it offers a large resistance force applied to the piston. This resistance dissipates energy quickly, reducing the amplitude of oscillations over time. The high viscosity means that when the piston moves, a significant amount of energy is lost as work done against the viscous drag, leading to a rapid decrease in oscillation energy.