Let the length of the wire be l and the maximum angle of displacement be θ0.
When the load is released from angle θ0, it falls through a vertical height h=l−lcosθ0=l(1−cosθ0).
By conservation of mechanical energy, the kinetic energy at the lowest (equilibrium) position is equal to the loss in potential energy:
21mv2=mgh=mgl(1−cosθ0)
v2=2gl(1−cosθ0)
At the equilibrium position, the tension T is maximum and provides the required centripetal force:
T−mg=lmv2
T=mg+lm[2gl(1−cosθ0)]
T=mg+2mg(1−cosθ0)=mg(3−2cosθ0)
Given maximum tension Tmax=2940 N, mass m=150 kg, and taking acceleration due to gravity g=9.8 m/s2:
2940=150×9.8×(3−2cosθ0)
2940=1470(3−2cosθ0)
2=3−2cosθ0
2cosθ0=1⟹cosθ0=21
θ0=60∘