Two geekie physics students with a combined mass of 131 kg jump into their old car to run out for some late night pizza. The distance between the front and back axles of the car is 2.9 m. When they get in the car, the springs compress a total of 9.3 cm. On their way to the Pizza Hut, when they go over a bump, the car oscillates up and down with a period of 1.6 seconds.

(a) What is mass of the car?

Can you guys figure it out??
i got 2020.185 for K constant and then i used the formula m=kt^2/4pi^2 but that is wrong and it's giving me the same mass help or guide me please.

From the compression deltaX of the springs when they get in, you know that the spring constant of the suspension system is

k = F/deltaX = 131*g*/0.093 = 13800 N/m

The oscillation period is 2 pi sqrt [(M+m)/k] = 1.6
where M is the car weight and m is the additional weight of the passengers.

Solve for M+m and them subtract m

(M+m)/k = 6.48*10^-2 s^2

M+m = 895 kg
m = 764 kg

To find the mass of the car, we can use the formula for the period of oscillation of a mass-spring system:

T = 2π√(m/k)

Where:
T is the period of oscillation (given as 1.6 seconds)
m is the mass of the car (what we are trying to find)
k is the spring constant

To find the spring constant (k), we can use Hooke's Law:

F = -kx

Where:
F is the force applied to the spring (in this case, the weight of the two physics students, which is their combined mass multiplied by the acceleration due to gravity: F = m * g)
x is the displacement of the spring (given as the total compression of 9.3 cm, which is 0.093 m in SI units)

Since the weight of the students is given by F = m * g, we have:

m * g = k * x

Rearranging the equation for k, we get:

k = (m * g) / x

We can now substitute this value for k into the equation for the period of oscillation:

T = 2π√(m / [(m * g) / x])

Simplifying the expression inside the square root:

T = 2π√(x / g)

Now we can solve for m by squaring both sides of the equation and rearranging:

(m / [(m * g) / x]) = 4π^2 * (x / g)

Simplifying further:

m = [(m * g) / x] * 4π^2 * (x / g)

Canceling out common terms:

m = 4π^2 * [(m * g) / g^2] * x

Simplifying even further:

m = 4π^2 * m * (x / g)

Now we can solve for m by canceling out the m term on both sides:

1 = 4π^2 * (x / g)

Solving for m:

m = g / (4π^2 * (x / g))

m = g^2 / (4π^2 * x)

Substituting the given values:
g = 9.8 m/s^2 (acceleration due to gravity)
x = 0.093 m (spring compression)

m = (9.8)^2 / (4π^2 * 0.093)
m ≈ 55.22 kg

Therefore, the mass of the car is approximately 55.22 kg.

To determine the mass of the car, we can use the equation for the period of an oscillating system:

T = 2π√(m/k)

where T is the period, m is the mass, and k is the spring constant.

Given that the period is 1.6 seconds, we can rearrange the formula to solve for m:

m = (T^2 * k) / (4π^2)

Now, let's calculate the spring constant k:

The spring constant can be determined using Hooke's Law:

F = kx

where F is the force applied to the spring and x is the displacement from equilibrium.

In this case, the force applied to the springs is the weight of the students. The weight is given by:

F = mg

where m is the combined mass of the students (131 kg in this case) and g is the acceleration due to gravity (approximately 9.8 m/s^2).

The displacement from equilibrium is the compression of the springs, which is given as 9.3 cm. To convert this to meters, we divide by 100:

x = 9.3 cm / 100 = 0.093 m

Now, we can calculate the force applied to the springs:

F = (131 kg) * (9.8 m/s^2) ≈ 1283.8 N

Next, we can determine the spring constant:

k = F / x = 1283.8 N / 0.093 m ≈ 13826.9 N/m

Now that we have the spring constant, let's calculate the mass of the car:

m = (1.6 s)^2 * 13826.9 N/m / (4π^2) ≈ 1547.02 kg

Therefore, the mass of the car is approximately 1547.02 kg.