Final answer:
The angular frequency of oscillation for two identical masses each of 75 g connected by a spring of spring constant 35 N/m is approximately 21.6 rad/s.
Step-by-step explanation:
Finding the Angular Frequency of Oscillation
To find the angular frequency of oscillation for a system comprising two identical masses connected by a spring, we use the formula for the angular frequency of a mass-spring system:
ω = √(k/m)
where ω is the angular frequency, k is the spring constant, and m is the mass of one of the objects. Since there are two identical masses, the effective mass for the oscillation becomes (m1 + m2)/2. The given mass is 75 g for each object, so m = (75 g + 75 g) / 2 = 75 g, which we convert to kilograms:
m = 75 g * 0.001 kg/g = 0.075 kg
The spring constant is given as 35 N/m. Now, substituting the values:
ω = √(35 N/m / 0.075 kg) = √(466.67 s⁻²)
ω ≈ 21.6 s⁻¹
Therefore, the angular frequency of the system is approximately 21.6 rad/s.