a spring has a 2.000x10^3 N/m spring constant.

how do you find the mass that will make it oscillate 5.0 times per second? 10.0 times per second?

Bxbd

To find the mass that will make the spring oscillate at a specific frequency, you can use the formula for the angular frequency of a mass-spring system and the relationship between angular frequency and frequency.

The angular frequency (ω) of a mass-spring system is given by the equation:

ω = √(k/m)

where:
- ω is the angular frequency (in radians per second),
- k is the spring constant (in N/m), and
- m is the mass (in kilograms).

To find the mass, we need to rearrange the formula and solve for m:

m = k / ω^2

1. To make the spring oscillate 5.0 times per second, we can calculate the angular frequency (ω) using the formula:

ω = 2πf

where:
- ω is the angular frequency (in radians per second),
- π is a constant (~3.14159), and
- f is the frequency (in cycles per second or Hertz).

Substituting 5.0 Hz for f, we have:

ω = 2π * 5.0 = 31.4 radians/second (approx.)

Now, substitute the known values into the rearranged formula for mass:

m = (2.000x10^3 N/m) / (31.4 radians/second)^2

m ≈ 2.04 kg

Therefore, to make the spring oscillate 5.0 times per second, the mass should be approximately 2.04 kg.

2. Similarly, to find the mass for 10.0 times per second, repeat the steps with the new frequency value:

ω = 2π * 10.0 = 62.8 radians/second (approx.)

m = (2.000x10^3 N/m) / (62.8 radians/second)^2

m ≈ 0.643 kg

Therefore, to make the spring oscillate 10.0 times per second, the mass should be approximately 0.643 kg.

change those frequencies to period (Period= 1/freq)

period=2PI*sqrt(m/k)

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