A compact car has a mass of 1200 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. b. What will be the car's oscillation frequency while carrying four 70 kg passengers?

Video transcript

Hey, everyone. So this problem is dealing with simple harmonic motion. Let's see what it's asking us. We have a motorcycle that weighs 300 kg with a coil spring on each wheel and the motorcycle's mass is evenly distributed over those two wheels. And therefore the two coils, the quails are identical. They both have a spring constant that's given here as 5.5 10, 10 to the fifth newtons per meter. The bike is transporting 2 65 kg riders. And we're asked to calculate the frequency of the oscillations of the motorcycle. And it just tells us to consider the motorcycle is in simple harmonic motion. So our multiple choice answers here are a eight Hertz B 16 Hertz C 25 Hertz or D 50 Hertz. So the key to solving this problem is we're calling it for simple harmonic motion. The period which is equal to one over the frequency is given by the equation two pi multiplied by the square root of mass divided by the spring constant. So we are looking for the frequency, that's what we need to solve for this problem. So substituting the frequency into this equation for um T R period, we get frequencies equal to one divided by two pi multiplied by the square root of K divided by M. And so when we look at these terms, we have K given to us in the problem and M we need to do just a little bit of work to find. So we are looking at a single spring. So what we need to find is the map that is acting or that is being supported by just the one spring. So our total mass is going to be equal to the bike, just 300 kg plus each of the riders. So 65 kg 65 kg. So our total mass is kg, which means the mass over a single spring is going to be kg. It's just the total mass divided by two. And so now we do have everything we need to solve for our frequency. So frequency again is equal to one divided by two pi multiplied by K. Our spring constant was given us 5.5 times 10 to the fifth newtons per meter divided by our mass. 215 kg, plug that into our calculator and we get eight Hertz. And so that is the answer to this problem and it aligns with answer choice. A that's all we have for this one. We'll see you in the next video.