Find the speed of oscillation of an ideal spring and mass system, given the mass is 1.5kg and the spring constant is 20N/m. The distance travelled in one complete oscillation is 10cm. Find the speed of the oscillation.
To find the speed of oscillation of an ideal spring and mass system, we can use the formula:
v = ω * A,
where:
- v is the speed of oscillation,
- ω is the angular frequency of oscillation,
- A is the amplitude of oscillation.
First, let's find the angular frequency (ω) of the system. The angular frequency is given by the formula:
ω = √(k / m),
where:
- k is the spring constant,
- m is the mass.
Given:
- k = 20 N/m,
- m = 1.5 kg.
Substituting these values into the formula, we get:
ω = √(20 N/m / 1.5 kg).
Calculating this, we find:
ω = √(13.333 N/kg).
Next, let's find the amplitude (A) of the oscillation. The amplitude is the maximum displacement of the mass from the equilibrium position. In this case, the distance travelled in one complete oscillation is given as 10 cm.
Remember that 1 meter (m) is equal to 100 centimeters (cm). So, we convert the distance to meters:
A = 10 cm * (1 m / 100 cm) = 0.1 m.
Finally, substituting the values of ω and A into the speed formula, we get:
v = √(13.333 N/kg) * 0.1 m.
Calculating this, we find:
v ≈ 1.155 m/s.
Therefore, the speed of the oscillation is approximately 1.155 m/s.