mass of 0.2 kg is attached to a spring of negligible mass. I the mass executes simple harmonic motion with a period of 0.5 s, what will be the spring constant/
Can I use the following formula to solve this problem
k = (4pi square x mass) / T square
yes, use that.
Yes, you can use the formula you mentioned to solve this problem.
To find the spring constant (k) of a spring-mass system, you can use the formula:
k = (4π² * m) / T²
where:
- k is the spring constant (measured in N/m)
- π (pi) is a mathematical constant approximately equal to 3.14159
- m is the mass of the object attached to the spring (in kg)
- T is the period of the simple harmonic motion (in seconds)
In this case, you are given:
- The mass (m) = 0.2 kg
- The period (T) = 0.5 s
You can substitute these values into the formula and calculate the spring constant (k).
First, square the value of the period (0.5 s) to get T²:
T² = 0.5² = 0.25 s²
Then, substitute the values into the formula:
k = (4π² * 0.2) / 0.25
Next, calculate 4π² * 0.2:
4π² * 0.2 ≈ 3.98
Finally, divide the result by 0.25:
k ≈ 3.98 / 0.25 ≈ 15.92 N/m
Therefore, the spring constant (k) is approximately 15.92 N/m.