In the above system the spring constant is k = 25 N/m and the mass on the spring is 100 grams.

What are the angular velocity and the harmonic frequency if we triple the mass?

Round your answer to one (1) decimal place. Do not enter units. Example: 33.4

Question

In the above system the spring constant is k = 25 N/m and the mass on the spring is 100 grams.

What are the  angular velocity and the harmonic frequency if we triple the mass?

Round your answer to one (1) decimal place. Do not enter units. Example: 33.4

BlackTom AI · Accepted Answer

We start by identifying the given quantities: spring constant k = 25 N/m and initial mass m0 = 100 g = 0.100 kg. When the mass is tripled, the new mass is m = 3 × 0.100 kg = 0.300 kg.

Next, recall the angular frequency for a mass-spring system: ω = sqrt(k / m).

Compute ω with the new mass: ω = sqrt(25 / 0.300) = sqrt(83.333... ) ≈ 9.1287 rad/s. Rounding to one decimal place gives 9.1.

The harmonic (linear) frequency is f = ω / (2π). Using ω ≈ 9.1287 rad/s, f ≈ 9.1287 / 6.2832 ≈ 1.453 Hz. Rounding to one decimal place yields 1.5.

Therefore, the pair for the angular velocity and harmonic frequency, each rounded to one decimal place and without units, is 9.1 and 1.5 respectively.

Tip: rounding at each step helps avoid carrying extra digits into the final result, which is especially important when the prompt demands a single-decimal answer.

ENGR-216:501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,PHYS-216:501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524 Angular Mo and Harmonics

In the above system the spring constant is k = 25 N/m and the mass on the spring is 100 grams. What are the angular velocity and the harmonic frequency if we triple the mass? Round your answer to one (1) decimal place. Do not enter units. Example: 33.4

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